
pip install sktime

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pip install pmdarima

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Note: you may need to restart the kernel to use updated packages.


# Basic libraries
import warnings
warnings.filterwarnings('ignore')
import numpy as np
import pandas as pd
import datetime as dt
import matplotlib.pyplot as plt
import seaborn as sns
import os
from scipy import stats
from sktime.forecasting.all import temporal_train_test_split
from tensorflow import keras
import tensorflow as tf
import statsmodels.api as sm
from scipy.special import inv_boxcox
from sktime.performance_metrics.forecasting import mean_absolute_error
from sktime.performance_metrics.forecasting import mean_squared_error
from sktime.performance_metrics.forecasting import mean_absolute_percentage_error
from pmdarima.arima import auto_arima
import warnings
warnings.filterwarnings('ignore')


# Function for simple EDA
def df_overview(df):
    dtype_df = pd.DataFrame(df.dtypes, columns=["type"])
    numNA_df = pd.DataFrame(df.isnull().sum(), columns=["NAs"])
    nunique_df = pd.DataFrame(df.nunique(), columns=["unique"])
    describe_df = df.describe(include="all").T[["count", "min", "max", "mean"]]
    overview_df = pd.concat([dtype_df, numNA_df, nunique_df, describe_df], axis=1)
    overview_df.fillna(value="-", inplace=True)
    overview_df["count"] =  overview_df["count"].astype(int)
    overview_df["(%)"] = round((overview_df["NAs"]/df.shape[0])*100, 1)
    overview_df.loc[overview_df["NAs"] == 0, "(%)"] = "-"
    overview_df = overview_df.reindex(columns=["type", "count", "NAs", "(%)", "unique", "min", "max", "mean"])
    display(overview_df)


# Libraries for ACF & PACF
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

# Libraries for ADF & KPSS
from statsmodels.tsa.stattools import kpss, adfuller

# Library for Ljung-Box test
from statsmodels.stats.diagnostic import acorr_ljungbox

# Function to run both ADF and KPSS tests
def adf_kpss(timeseries, alpha=0.05):
  # ADF test
  adf_test = adfuller(timeseries, autolag="AIC")
  adf_result = pd.Series(adf_test[0:3],
                         index=["Test Statistic", "p-value", "Lags Used"])
  for key, value in adf_test[4].items():
    adf_result["Critical Value (%s)"%key] = value

  # KPSS test with regression="c"
  kpss_test_c = kpss(timeseries, regression="c")
  kpss_result_c = pd.Series(kpss_test_c[0:3],
                          index=["Test Statistic", "p-value", "Lags Used"])
  for key, value in kpss_test_c[3].items():
    kpss_result_c["Critical Value (%s)"%key] = value

  # KPSS test with regression="ct"
  kpss_test_ct = kpss(timeseries, regression="ct")
  kpss_result_ct = pd.Series(kpss_test_ct[0:3],
                          index=["Test Statistic", "p-value", "Lags Used"])
  for key, value in kpss_test_ct[3].items():
    kpss_result_ct["Critical Value (%s)"%key] = value
  
  # Result table
  result = pd.concat([adf_result, kpss_result_c, kpss_result_ct], axis=1).dropna()
  result.columns = ["ADF", "KPSS('c')", "KPSS('ct')"]

  # Determine whether timeseries is stationary or not from each test
  adf_pval = result.loc["p-value", "ADF"]
  adf_bool = adf_pval <= alpha
  print(f"stationarity from ADF test: {adf_bool}")

  kpss_c_pval = result.loc["p-value", "KPSS('c')"]
  kpss_c_bool = kpss_c_pval >= alpha
  print(f"stationarity from KPSS test('c'): {kpss_c_bool}")

  kpss_ct_pval = result.loc["p-value", "KPSS('ct')"]
  kpss_ct_bool = kpss_ct_pval >= alpha
  print(f"stationarity from KPSS test('ct'): {kpss_ct_bool}\n")
  
  # Show the result table
  display(result)


# Function to show lineplot, histogram, and ADF/KPSS result for series
def create_plot_adf_kpss(timeseries, title, alpha=0.05):
    fig, axes = plt.subplots(1,2, figsize=(16,5))
    axes[0] = timeseries.plot(ax=axes[0])
    axes[0].set_title(title)
    axes[0].grid()
    axes[1].hist(timeseries)
    axes[1].set_title(f"Histogram of {title}")
    plt.show()

    print(f"\nADF/KPSS tests for {title} (alpha={alpha}):")
    adf_kpss(timeseries, alpha)


# acf, pacf Import
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

# Function to plot ACF/PACF and PACF for timeseries
def plot_acf_pacf(timeseries, title, lags=50, auto_ylims=True):
    fig, axes = plt.subplots(2,1, figsize=(16,10))
    plot_acf(timeseries, lags=lags, title=f"ACF for {title}", ax=axes[0], zero=False, auto_ylims=auto_ylims)
    axes[0].grid()
    plot_pacf(timeseries, lags=lags, title=f"PACF for {title}", ax=axes[1], zero=False, auto_ylims=auto_ylims)
    axes[1].grid()
    plt.show()


# Libraries for metrics
from sktime.performance_metrics.forecasting import MeanAbsolutePercentageError
from sktime.performance_metrics.forecasting import MeanAbsoluteError
from sktime.performance_metrics.forecasting import MeanSquaredError

def calc_metrics(y_true, y_pred, round_value=4, print_result=True, return_dict=False):
    # Create dict
    metrics_dict = dict()

    # MAE
    mae = MeanAbsoluteError()
    metrics_dict["MAE"] = mae(y_true, y_pred)

    # MSE
    mse = MeanSquaredError(square_root=False)
    metrics_dict["MSE"] = mse(y_true, y_pred)

    # MAPE
    mape = MeanAbsolutePercentageError(symmetric=False)
    metrics_dict["MAPE"] = mape(y_true, y_pred)

    # SMAPE
    smape = MeanAbsolutePercentageError(symmetric=True)
    metrics_dict["sMAPE"] = smape(y_true, y_pred)

    # MASE(for monthly seasonal timeseries)
    naive_foacast_error = y_true.diff(12).mean()
    metrics_dict["MASE"] = mae(y_true, y_pred)/naive_foacast_error

    # Round values
    for key, value in metrics_dict.items():
        metrics_dict[key] = round(value, round_value)

    # Print result or return metrics_dict
    if print_result:
        print("Test Error Metrics")
        for key, value in metrics_dict.items():
            print(f"{key}: {value}")
    if return_dict:
        return metrics_dict


def make_plot(train_y, test_y, pred_y, title):
    fig, ax = plt.subplots(figsize=(16,5))
    train_y.plot(ax=ax, label="Training")
    test_y.plot(ax=ax, label="Test", color="black")
    pred_y.plot(ax=ax, label=title, linestyle="dashed")
    plt.legend()
    plt.show()


PATH = "/Users/azizhazeinita/Project/Tokyo Gas/"
df_listings = pd.read_csv(PATH + 'stock_list.csv')
df_stock_price = pd.read_csv(PATH + 'stock_prices.csv')


# Apply => No NAs, dtype:int or float
print("df_stock_price")
df_overview(df_stock_price)
print("\ndf_listings")
df_overview(df_listings)

df_stock_price

df_listings


# Function to load the data and create series
def load_(path, f_name, col_name):
    # Load dataframe
    df = pd.read_csv(os.path.join(path, f_name))
    df["Date"] = pd.to_datetime(df["Date"])
    df = df.set_index(df["Date"])
    df.columns = ["Date", col_name]

    # Extract needed external data (other than "Date" column) as series
    series = df[col_name]

    # Return both df and series
    return df, series


# Path
PATH_ = "/Users/azizhazeinita/Project/Tokyo Gas/external_data/"

# GDP
gdp, gdp_s = load_(PATH_, "jp_gdp.csv", "jp_gdp")

# Unemployment rate
unemp, unemp_s = load_(PATH_, "jp_unemp.csv", "jp_unemp")

# Oil price
oil, oil_s = load_(PATH_, "oil.csv", "oil")

# JPY/USD
usdjpy, usdjpy_s = load_(PATH_, "usdjpy.csv", "usdjpy")

# Interest Rate (long-term)
interest, interest_s = load_(PATH_, "jp_interest_rate_long.csv", "jp_i")

# Nikkei 225 index
n225, n225_s = load_(PATH_, "jp_n225.csv", "n225")


temp = df_listings.groupby('33SectorName').count().sort_values('SecuritiesCode', ascending=False)
temp.head(10)


# The number of companies in each industry
temp = df_listings.groupby('33SectorName').count().sort_values('SecuritiesCode', ascending=False)

plt.figure(figsize=(20,15))
sns.barplot(y = temp.index, x = temp['Name'], orient="h",
            palette = sns.color_palette("GnBu_r"))
plt.ylabel('Sector Name', fontsize = 14)
plt.xlabel('Count', fontsize = 10)
plt.title('Count of Industry')
plt.tick_params(axis='both', which='major', labelsize=20)
plt.show()


#The top 10 industry intern of nunmber
temp2 = df_listings.groupby('33SectorName').count().sort_values('SecuritiesCode', ascending=False).head(10)

plt.figure(figsize=(20,15))
sns.barplot(y = temp2.index, x = temp2['Name'], orient="h",
            palette = sns.color_palette("GnBu_r"))
plt.ylabel('Sector Name', fontsize = 20)
plt.xlabel('Count', fontsize = 20)
plt.title('Top 10 Industry', fontsize = 20)
plt.tick_params(axis='both', which='major', labelsize=20)
plt.show()


def create_df_energy(df_raw=df_listings):
    # Elec & Gas
    df_gas = df_raw[(df_raw["33SectorName"] == "Electric Power and Gas")]
    df_gas.loc[df_gas["Name"].str.contains("Power"), "Category"] = "Electric Utility"
    df_gas.loc[df_gas["Name"].str.contains("GAS"), "Category"] = "Gas Utility"
    df_gas.loc[df_gas["Name"].str.contains("METAWATER"), "Category"] = "Other"
    df_gas["Category"] = df_gas["Category"].fillna("Other Electricity Service")

    # Oil & Coal
    df_oil = df_raw[(df_raw["33SectorName"] == "Oil and Coal Products")]
    oil_company = ["ENEOS Holdings,Inc.", "Idemitsu Kosan Co.,Ltd.", "COSMO ENERGY HOLDINGS COMPANY,LIMITED",
                   "TonenGeneral Sekiyu K.K.", "Fuji Oil Company,Ltd.", "TOA OIL COMPANY,LIMITED"]
    df_oil.loc[df_oil["Name"].isin(oil_company), "Category"] = "Oil"
    df_oil.loc[df_oil["Name"]=="VITEC HOLDINGS CO.,LTD.", "Category"] = "Other"
    df_oil["Category"] = df_oil["Category"].fillna("Oil Products Manufacturer")

    # Merge
    df_energy = pd.concat([df_gas, df_oil], axis=0)

    return df_energy

df_energy = create_df_energy()
df_energy[["SecuritiesCode", "Name", "33SectorName", "Category", "Section/Products"]]


df_energy.shape

(38, 17)


# Merge df_stock_price & df_energy
df = pd.merge(
    left=df_stock_price,
    right=df_energy[["SecuritiesCode", "Name", "33SectorName", "Category", "Section/Products"]],
    on="SecuritiesCode", how="left"
    ).dropna(subset=["Name"])
df["Date"] = pd.to_datetime(df["Date"])
df = df.set_index(df["Date"], drop=True)


# Comapnies not included in stock_price.csv
df_energy[df_energy["Name"].isin(list(set(df_energy["Name"].unique()).difference(set(df["Name"].unique()))))]


fig, ax = plt.subplots(figsize=(16,8))
for c in df.loc[df["Category"]=="Electric Utility", "Name"].unique():
    df.loc[df["Name"]==c, "Close"].plot(ax=ax, label=c)
ax.legend(loc="upper right")
ax.set_title("Electric Utilities")
plt.show()


fig, ax = plt.subplots(figsize=(16,8))
for c in df.loc[df["Category"]=="Gas Utility", "Name"].unique():
    df.loc[df["Name"]==c, "Close"].plot(ax=ax, label=c)
ax.legend(loc="upper left")
ax.set_title("Gas Utilities")
plt.show()


fig, ax = plt.subplots(figsize=(16,8))
for c in df.loc[df["Category"]=="Oil", "Name"].unique():
    df.loc[df["Name"]==c, "Close"].plot(ax=ax, label=c)
ax.legend(loc="upper left")
ax.set_title("Oil Companies")
plt.show()


fig, ax = plt.subplots(figsize=(16,8))
for c in df.loc[df["Category"].isin(["Other Electricity Service", "Oil Products Manufacturer", "Other"]), "Name"].unique():
    df.loc[df["Name"]==c, "Close"].plot(ax=ax, label=c)
ax.legend(loc="upper left")
ax.set_title("Other")
plt.show()


main5 = df.copy().loc[df["SecuritiesCode"].isin([9501, 9503, 9531, 9532, 5020]), ["Date", "SecuritiesCode", "Close", "Name", "Category"]]
main5.loc[main5["Name"]=="ENEOS Holdings,Inc.", "Name"] = "ENEOS"
main5.loc[main5["Name"]=="Tokyo Electric Power Company Holdings,Incorporated", "Name"] = "Tokyo Electric Power"
main5.loc[main5["Name"]=="The Kansai Electric Power Company,Incorporated", "Name"] = "Kansai Electric Power"
main5.loc[main5["Name"]=="TOKYO GAS CO.,LTD.", "Name"] = "Tokyo Gas"
main5.loc[main5["Name"]=="OSAKA GAS CO.,LTD.", "Name"] = "Osaka Gas"


fig, ax = plt.subplots(figsize=(16,8))
for c in main5["Name"].unique():
    main5.loc[main5["Name"]==c, "Close"].plot(ax=ax, label=c)
ax.legend(loc="upper left")
ax.set_title("Main Utilities and Oil Companies", fontsize = 20)
plt.show()


# Tokyo Gas & Osaka Gas change unit of stocks from 9/27/2017 (5 shares to 1 share)
main5.loc[(main5["SecuritiesCode"].isin([9531, 9532])) & (main5.index.year==2017) & (main5.index.month==9) & (main5.index.day>20)].sort_values("SecuritiesCode")


main5["Adjusted Close"] = main5["Close"]
main5.loc[(main5["SecuritiesCode"].isin([9531, 9532])) & (main5["Date"] < dt.datetime(2017,9,27)), "Adjusted Close"] = main5.loc[(main5["SecuritiesCode"].isin([9531, 9532])) & (main5["Date"] < dt.datetime(2017,9,27)), "Adjusted Close"]*5


fig, ax = plt.subplots(figsize=(16,8))
for c in main5["Name"].unique():
    main5.loc[main5["Name"]==c, "Adjusted Close"].plot(ax=ax, label=c)
ax.legend(loc="upper right")
ax.set_title("Main Utilities and Oil Companies")
plt.show()


# See correlation
main5_corr = main5.copy()
main5_corr = main5_corr.pivot(index=["Date"], columns="Name", values="Adjusted Close")
sns.pairplot(main5_corr)
plt.show()
sns.heatmap(main5_corr.corr(), annot=True)
plt.show()


# Function to create plot to see seasonality
def check_seasonality(timeseries, title, ax=None):
    df = pd.DataFrame(timeseries)
    df.columns = ["price"]
    df["year"] = df.index.year
    df["dayofyear"] = df.index.dayofyear

    if ax==None:
        fig, ax = plt.subplots(figsize=(16,8))
        sns.lineplot("dayofyear", "price", data=df, hue="year", ax=ax, legend=None)
        ax.set_title(f"Seasonal Plot of {title}")
        ax.set_xlabel("Day of Year")
        ax.set_ylabel(title)
        ax.grid()
        plt.show()
    else:
        sns.lineplot("dayofyear", "price", data=df, hue="year", ax=ax, legend=None)
        ax.set_title(f"Seasonal Plot of {title}")
        ax.set_xlabel("Day of Year")
        ax.set_ylabel(title)
        ax.grid()
        return ax

# Check seasonality for main 5 companies => Seem no seasonality
fig, axes = plt.subplots(3,2, figsize=(16,10), tight_layout=True)
axes_flat = [s for sublist in axes for s in sublist]
for i, name in enumerate(main5["Name"].unique()):
    check_seasonality(main5.loc[main5["Name"]==name, "Adjusted Close"], name, ax=axes_flat[i])
plt.show()


fig, ax = plt.subplots(figsize=(16,8))
for c in main5["Name"].unique():
    main5.loc[main5["Name"]==c, "Adjusted Close"].plot(ax=ax, label=c)
ax.set_title("Main Utilities and Oil Companies")
ax.plot(n225["n225"]/10, color="Black", label="Nikkei Stock Index (/10)")
ax.plot(usdjpy["usdjpy"]*10, color="grey", label="USDJPY (*10)")
ax.plot(oil["oil"]*50, color="yellow", label="WTI Oil Price (*50)")
ax.legend(loc="upper left")
ax.set_ylim(0,)
plt.show()


tokyo_gas = main5.loc[main5["Name"]=="Tokyo Gas", "Adjusted Close"]
tokyo_gas = tokyo_gas.dropna()
tokyo_gas.name = "Tokyo Gas"


# Check stationarity
create_plot_adf_kpss(tokyo_gas, "Tokyo_Gas_original")

ADF/KPSS tests for Tokyo_Gas_original (alpha=0.05):
stationarity from ADF test: False
stationarity from KPSS test('c'): False
stationarity from KPSS test('ct'): False


# Take first difference
tokyo_gas_diff = tokyo_gas.diff().dropna()


# Check stationarity
create_plot_adf_kpss(tokyo_gas_diff, "Tokyo Gas (diff(1))")

ADF/KPSS tests for Tokyo Gas (diff(1)) (alpha=0.05):
stationarity from ADF test: True
stationarity from KPSS test('c'): True
stationarity from KPSS test('ct'): True


plot_acf_pacf(tokyo_gas_diff, "tokyo_gas_dif(diff(1))", lags=50)


# Using data before 2020 as training
y_train = tokyo_gas[tokyo_gas.index.year!=2021]
y_test = tokyo_gas[tokyo_gas.index.year==2021]


arima_model = auto_arima(y_train, start_p=0, d=1, start_q=0, seasonal=False)
print(arima_model.summary())

                               SARIMAX Results                                
==============================================================================
Dep. Variable:                      y   No. Observations:                  975
Model:               SARIMAX(4, 1, 1)   Log Likelihood               -4942.886
Date:                Wed, 05 Oct 2022   AIC                           9897.771
Time:                        16:54:34   BIC                           9927.060
Sample:                             0   HQIC                          9908.917
                                - 975                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
ar.L1         -0.7169      0.103     -6.935      0.000      -0.920      -0.514
ar.L2         -0.0480      0.029     -1.646      0.100      -0.105       0.009
ar.L3         -0.1299      0.034     -3.864      0.000      -0.196      -0.064
ar.L4         -0.1585      0.027     -5.860      0.000      -0.211      -0.105
ma.L1          0.7350      0.104      7.064      0.000       0.531       0.939
sigma2      1497.6393     47.041     31.837      0.000    1405.440    1589.839
===================================================================================
Ljung-Box (L1) (Q):                   0.01   Jarque-Bera (JB):               378.52
Prob(Q):                              0.92   Prob(JB):                         0.00
Heteroskedasticity (H):               1.43   Skew:                             0.07
Prob(H) (two-sided):                  0.00   Kurtosis:                         6.05
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).


y_pred_arima110 = arima_model.predict(len(y_test))
y_pred_arima110 = pd.Series(y_pred_arima110)
y_pred_arima110.index = y_test.index
fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_arima110.plot(ax=ax, label="ARIMA(1,1,0)", linestyle="dashed")
plt.legend()
plt.show()


arima110_metrics = calc_metrics(y_test, y_pred_arima110, return_dict=True)

Test Error Metrics
MAE: 203.792
MSE: 58725.0992
MAPE: 0.0978
sMAPE: 0.0914
MASE: -8.7564


# Merge data and fill NAs with interpolation
tokyo_gas_m = pd.concat([tokyo_gas, oil_s, n225_s], axis=1)
tokyo_gas_m = tokyo_gas_m.dropna(subset=["Tokyo Gas"])
tokyo_gas_m["oil"] = tokyo_gas_m["oil"].interpolate()
tokyo_gas_m["n225"] = tokyo_gas_m["n225"].interpolate()
tokyo_gas_m


# Using data before 2020 as training
X_train_oil = tokyo_gas_m.loc[tokyo_gas_m.index.year!=2021, "oil"]
X_test_oil = tokyo_gas_m.loc[tokyo_gas_m.index.year==2021, "oil"]


arimax_oil = auto_arima(y_train, X=X_train_oil.values.reshape(-1, 1), start_p=0, d=1, start_q=0, seasonal=False)
print(arimax_oil.summary())

                               SARIMAX Results                                
==============================================================================
Dep. Variable:                      y   No. Observations:                  975
Model:               SARIMAX(4, 1, 1)   Log Likelihood               -4942.464
Date:                Wed, 05 Oct 2022   AIC                           9898.927
Time:                        16:55:29   BIC                           9933.097
Sample:                             0   HQIC                          9911.931
                                - 975                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
x1             0.4327      0.776      0.558      0.577      -1.088       1.953
ar.L1         -0.7055      0.109     -6.459      0.000      -0.920      -0.491
ar.L2         -0.0480      0.029     -1.655      0.098      -0.105       0.009
ar.L3         -0.1269      0.034     -3.781      0.000      -0.193      -0.061
ar.L4         -0.1551      0.027     -5.706      0.000      -0.208      -0.102
ma.L1          0.7242      0.110      6.577      0.000       0.508       0.940
sigma2      1496.3368     47.401     31.568      0.000    1403.433    1589.241
===================================================================================
Ljung-Box (L1) (Q):                   0.01   Jarque-Bera (JB):               392.25
Prob(Q):                              0.92   Prob(JB):                         0.00
Heteroskedasticity (H):               1.43   Skew:                             0.08
Prob(H) (two-sided):                  0.00   Kurtosis:                         6.10
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).


y_pred_arimax110_oil = arimax_oil.predict(len(y_test), X=X_test_oil.values.reshape(-1, 1))
y_pred_arimax110_oil = pd.Series(y_pred_arimax110_oil)
y_pred_arimax110_oil.index = y_test.index
fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_arimax110_oil.plot(ax=ax, label="ARIMAX(1,1,0) with Oil Price", linestyle="dashed")
plt.legend()
plt.show()


arima110_oil_metrics = calc_metrics(y_test, y_pred_arimax110_oil, return_dict=True)

Test Error Metrics
MAE: 211.5135
MSE: 63002.5703
MAPE: 0.1015
sMAPE: 0.0946
MASE: -9.0882


# Using data before 2020 as training
X_train_n225 = tokyo_gas_m.loc[tokyo_gas_m.index.year!=2021, "n225"]
X_test_n225 = tokyo_gas_m.loc[tokyo_gas_m.index.year==2021, "n225"]


arimax_n225 = auto_arima(y_train, X=X_train_n225.values.reshape(-1, 1), start_p=0, d=1, start_q=0, seasonal=False)
print(arimax_n225.summary())

                               SARIMAX Results                                
==============================================================================
Dep. Variable:                      y   No. Observations:                  975
Model:               SARIMAX(0, 1, 0)   Log Likelihood               -4876.087
Date:                Thu, 02 Jun 2022   AIC                           9756.175
Time:                        22:06:01   BIC                           9765.938
Sample:                             0   HQIC                          9759.890
                                - 975                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
x1             0.0627      0.003     19.136      0.000       0.056       0.069
sigma2      1305.8502     37.170     35.132      0.000    1232.999    1378.701
===================================================================================
Ljung-Box (L1) (Q):                   0.60   Jarque-Bera (JB):               383.36
Prob(Q):                              0.44   Prob(JB):                         0.00
Heteroskedasticity (H):               1.56   Skew:                            -0.14
Prob(H) (two-sided):                  0.00   Kurtosis:                         6.06
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).


y_pred_arimax110_n225 = arimax_n225.predict(len(y_test), X=X_test_n225.values.reshape(-1, 1))
y_pred_arimax110_n225 = pd.Series(y_pred_arimax110_n225)
y_pred_arimax110_n225.index = y_test.index
fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_arimax110_n225.plot(ax=ax, label="ARIMAX(1,1,0) with Nikkei225", linestyle="dashed")
plt.legend()
plt.show()


arima110_n225_metrics = calc_metrics(y_test, y_pred_arimax110_n225, return_dict=True)

Test Error Metrics
MAE: 292.0734
MSE: 107173.8052
MAPE: 0.1389
sMAPE: 0.1274
MASE: -12.5497


# Using data before 2020 as training
X_train_oiln225 = tokyo_gas_m.loc[tokyo_gas_m.index.year!=2021, ["oil", "n225"]]
X_test_oiln225 = tokyo_gas_m.loc[tokyo_gas_m.index.year==2021, ["oil", "n225"]]


arimax_oiln225 = auto_arima(y_train, X=X_train_oiln225, start_p=0, d=1, start_q=0, seasonal=False)
print(arimax_oiln225.summary())

                               SARIMAX Results                                
==============================================================================
Dep. Variable:                      y   No. Observations:                  975
Model:               SARIMAX(0, 1, 0)   Log Likelihood               -4875.807
Date:                Thu, 02 Jun 2022   AIC                           9757.613
Time:                        22:06:03   BIC                           9772.258
Sample:                             0   HQIC                          9763.186
                                - 975                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
oil            0.3317      0.626      0.530      0.596      -0.895       1.559
n225           0.0625      0.003     19.055      0.000       0.056       0.069
sigma2      1305.1005     37.129     35.150      0.000    1232.328    1377.873
===================================================================================
Ljung-Box (L1) (Q):                   0.62   Jarque-Bera (JB):               385.62
Prob(Q):                              0.43   Prob(JB):                         0.00
Heteroskedasticity (H):               1.56   Skew:                            -0.14
Prob(H) (two-sided):                  0.00   Kurtosis:                         6.07
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).


y_pred_arimax110_oiln225 = arimax_oiln225.predict(len(y_test), X=X_test_oiln225)
y_pred_arimax110_oiln225 = pd.Series(y_pred_arimax110_oiln225)
y_pred_arimax110_oiln225.index = y_test.index
fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_arimax110_oiln225.plot(ax=ax, label="ARIMAX(1,1,0) with Oil Price & Nikkei225", linestyle="dashed")
plt.legend()
plt.show()


arima110_oiln225_metrics = calc_metrics(y_test, y_pred_arimax110_oiln225, return_dict=True)

Test Error Metrics
MAE: 298.0109
MSE: 111508.5736
MAPE: 0.1417
sMAPE: 0.1298
MASE: -12.8048


y_pred_arimax110_oiln225 = arimax_oiln225.predict(len(y_test), X=X_test_oiln225)
y_pred_arimax110_oiln225 = pd.Series(y_pred_arimax110_oiln225)
y_pred_arimax110_oiln225.index = y_test.index
fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_arima110.plot(ax=ax, label="ARIMA(1,1,0)", linestyle="solid")
y_pred_arimax110_oiln225.plot(ax=ax, label="ARIMAX(1,1,0) with Oil Price & Nikkei225", linestyle="dashed")
y_pred_arimax110_n225.plot(ax=ax, label="ARIMAX(1,1,0) with Nikkei225", linestyle="dashed", color = 'pink')
y_pred_arimax110_oil.plot(ax=ax, label="ARIMAX(1,1,0) with Oil Price", linestyle="dashed")
ax.set_title("ARIMA Model Comparison")
plt.legend()
plt.show()


# Take average of each week
tokyo_gas_weekly = tokyo_gas.resample("W").mean()
# Fill NA with interpolation
tokyo_gas_weekly = tokyo_gas_weekly.interpolate()


# Check stationarity
create_plot_adf_kpss(tokyo_gas_weekly, "tokyo_gas_weekly")

ADF/KPSS tests for tokyo_gas_weekly (alpha=0.05):
stationarity from ADF test: False
stationarity from KPSS test('c'): False
stationarity from KPSS test('ct'): False


# Check seasonality: No seasonality
df_season = pd.DataFrame(tokyo_gas_weekly)
df_season["year"] = df_season.index.year
df_season["week"] = df_season.index.week

# Line plot
fig, ax = plt.subplots(figsize=(15,6))
sns.lineplot("week", "Tokyo Gas", data=df_season, hue="year", ax=ax, legend=None)
ax.grid()
plt.show()


# Check stationarity for differenced data
create_plot_adf_kpss(tokyo_gas_weekly.diff().dropna(), "tokyo_gas_weekly")

ADF/KPSS tests for tokyo_gas_weekly (alpha=0.05):
stationarity from ADF test: True
stationarity from KPSS test('c'): True
stationarity from KPSS test('ct'): True


plot_acf_pacf(tokyo_gas_weekly.diff().dropna(), title = 'correlation check', lags=80)


# GDP
gdp_weekly = gdp_s.resample("W").mean().fillna(method="ffill")


# unemplyment rate
unemp_weekly = unemp_s.resample("W").mean().fillna(method="ffill")


# Oil Price
oil_weekly = oil_s.resample("W").mean()


# JPY/USD
usdjpy_weekly = usdjpy_s.resample("W").mean()


# Interest Rate (long-term)
interest_weekly = interest_s.resample("W").mean()


# Find NAs for interest_weekly
interest_weekly[interest_weekly.isna()]

Date
2019-05-05   NaN
Freq: W-SUN, Name: jp_i, dtype: float64


# Interpolation
interest_weekly = interest_weekly.interpolate()


# Nikkei 225 index
n225_weekly = n225_s.resample("W").mean()


# Find NAs
n225_weekly[n225_weekly.isna()]

Date
2019-05-05   NaN
Freq: W-SUN, Name: n225, dtype: float64


# Interpolation
n225_weekly = n225_weekly.interpolate()


# Merge data
weekly_m = pd.concat([tokyo_gas_weekly, gdp_weekly, unemp_weekly, oil_weekly, usdjpy_weekly, interest_weekly, n225_weekly], axis=1)

# Show rows with NAs => Need to fill jp_gdp (since last observation for gdp_weekly is for 2021-10-03)
weekly_m[weekly_m.isnull().any(axis=1)]


# Drop rows when "Tokyo Gas" is NA 
weekly_m = weekly_m.dropna(subset=["Tokyo Gas"])
# Fill NAs for jp_gdp with forward fill
weekly_m["jp_gdp"] = weekly_m["jp_gdp"].fillna(method="ffill")


# Plot external regressors
fig, axes = plt.subplots(2,3, figsize=(16,8), tight_layout=True)
axes_flat = [s for sublist in axes for s in sublist]
for i, c in enumerate(weekly_m.columns.difference(["Tokyo Gas"])):
    weekly_m[c].plot(ax=axes_flat[i])
    axes_flat[i].set_title(c)
plt.show()


# Using data before June 2021 as training
# One Year Prediction does not generate meaningul outcome, we decided to predict 6 monthes
df_train = weekly_m[:-23]
df_test = weekly_m[-23:]


# extract Tokyo Gas sereis as y_train and y_test
y_train = df_train["Tokyo Gas"]
y_test = df_test["Tokyo Gas"]


# Make prediction with arima model from pmdarima
def predict_from_arima(arima_model, test_y, test_X=None):
    y_pred = arima_model.predict(n_periods=len(test_y), X=test_X)
    y_pred = pd.Series(y_pred)
    y_pred.index = test_y.index
    return y_pred


# Make plot fro training/test/prediction
def make_plot(train_y, test_y, pred_y, title):
    fig, ax = plt.subplots(figsize=(16,5))
    train_y.plot(ax=ax, label="Training")
    test_y.plot(ax=ax, label="Test", color="black")
    pred_y.plot(ax=ax, label=title, linestyle="dashed")
    plt.legend()
    plt.show()


arima_uni = auto_arima(y_train, start_p=0, d=1, start_q=0, seasonal=False)
print(arima_uni.summary())

                               SARIMAX Results                                
==============================================================================
Dep. Variable:                      y   No. Observations:                  234
Model:               SARIMAX(2, 1, 2)   Log Likelihood               -1278.170
Date:                Thu, 02 Jun 2022   AIC                           2566.341
Time:                        22:06:13   BIC                           2583.596
Sample:                             0   HQIC                          2573.299
                                - 234                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
ar.L1          0.4466      0.170      2.630      0.009       0.114       0.779
ar.L2          0.3680      0.171      2.158      0.031       0.034       0.702
ma.L1         -0.2512      0.148     -1.694      0.090      -0.542       0.039
ma.L2         -0.6597      0.150     -4.389      0.000      -0.954      -0.365
sigma2      3401.4238    258.999     13.133      0.000    2893.795    3909.053
===================================================================================
Ljung-Box (L1) (Q):                   0.01   Jarque-Bera (JB):                50.41
Prob(Q):                              0.91   Prob(JB):                         0.00
Heteroskedasticity (H):               2.06   Skew:                            -0.55
Prob(H) (two-sided):                  0.00   Kurtosis:                         5.00
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).


print("ARIMA(0,1,1) / No-")
pred_arima011 = predict_from_arima(arima_uni, y_test)
make_plot(y_train, y_test, pred_arima011, "ARIMA(0,1,1) / No-")
metrics_arima011 = calc_metrics(y_test, pred_arima011, return_dict=True)

ARIMA(0,1,1) / No-

Test Error Metrics
MAE: 131.9129
MSE: 28228.7658
MAPE: 0.0661
sMAPE: 0.0627
MASE: -1.1125


arimax_n225 = auto_arima(y_train, X=df_train[["n225"]], start_p=0, d=1, start_q=0, seasonal=False)
print(arimax_n225.summary())

                               SARIMAX Results                                
==============================================================================
Dep. Variable:                      y   No. Observations:                  234
Model:               SARIMAX(1, 1, 1)   Log Likelihood               -1273.925
Date:                Thu, 02 Jun 2022   AIC                           2555.851
Time:                        22:06:20   BIC                           2569.655
Sample:                    01-08-2017   HQIC                          2561.417
                         - 06-27-2021                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
n225           0.0303      0.006      4.702      0.000       0.018       0.043
ar.L1         -0.4806      0.168     -2.854      0.004      -0.811      -0.151
ma.L1          0.7074      0.147      4.811      0.000       0.419       0.996
sigma2      3283.1021    205.844     15.950      0.000    2879.656    3686.548
===================================================================================
Ljung-Box (L1) (Q):                   0.01   Jarque-Bera (JB):               108.07
Prob(Q):                              0.94   Prob(JB):                         0.00
Heteroskedasticity (H):               2.35   Skew:                            -0.63
Prob(H) (two-sided):                  0.00   Kurtosis:                         6.09
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).


print("ARIMAX(0,1,1) / n225")
pred_arimax011_n225 = predict_from_arima(arimax_n225, y_test, test_X=df_test[["n225"]])
make_plot(y_train, y_test, pred_arimax011_n225, "ARIMAX(0,1,1)/n225")
metrics_arimax011_n225 = calc_metrics(y_test, pred_arimax011_n225, return_dict=True)

ARIMAX(0,1,1) / n225

Test Error Metrics
MAE: 78.5779
MSE: 10447.2298
MAPE: 0.0393
sMAPE: 0.0382
MASE: -0.6627


arimax_oil= auto_arima(y_train, X=df_train[["oil"]], start_p=0, d=1, start_q=0, seasonal=False)
print(arimax_oil.summary())

                               SARIMAX Results                                
==============================================================================
Dep. Variable:                      y   No. Observations:                  234
Model:               SARIMAX(2, 1, 2)   Log Likelihood               -1278.155
Date:                Thu, 02 Jun 2022   AIC                           2568.310
Time:                        22:06:32   BIC                           2589.016
Sample:                    01-08-2017   HQIC                          2576.659
                         - 06-27-2021                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
oil           -0.2549      1.125     -0.227      0.821      -2.460       1.950
ar.L1          0.4455      0.169      2.630      0.009       0.114       0.778
ar.L2          0.3680      0.172      2.139      0.032       0.031       0.705
ma.L1         -0.2504      0.148     -1.692      0.091      -0.541       0.040
ma.L2         -0.6600      0.150     -4.390      0.000      -0.955      -0.365
sigma2      3401.0397    259.039     13.129      0.000    2893.332    3908.748
===================================================================================
Ljung-Box (L1) (Q):                   0.01   Jarque-Bera (JB):                49.46
Prob(Q):                              0.91   Prob(JB):                         0.00
Heteroskedasticity (H):               2.05   Skew:                            -0.54
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.98
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).


print("ARIMAX(0,1,1) / oil&usdjpy")
pred_arimax011_oil = predict_from_arima(arimax_oil, y_test, test_X=df_test[["oil"]])
make_plot(y_train, y_test, pred_arimax011_oil, "ARIMAX(0,1,1)/oil")
metrics_arimax011_oil= calc_metrics(y_test, pred_arimax011_oil, return_dict=True)

ARIMAX(0,1,1) / oil&usdjpy

Test Error Metrics
MAE: 129.9804
MSE: 27404.4503
MAPE: 0.0652
sMAPE: 0.0618
MASE: -1.0962


arimax_all = auto_arima(y_train, X=df_train[df_train.columns.difference(["Tokyo Gas"])], start_p=0, d=1, start_q=0, seasonal=False)
print(arimax_all.summary())

                               SARIMAX Results                                
==============================================================================
Dep. Variable:                      y   No. Observations:                  234
Model:               SARIMAX(1, 1, 1)   Log Likelihood               -1271.564
Date:                Thu, 02 Jun 2022   AIC                           2561.128
Time:                        22:06:42   BIC                           2592.187
Sample:                    01-08-2017   HQIC                          2573.652
                         - 06-27-2021                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
jp_gdp        -0.0020      0.001     -2.732      0.006      -0.004      -0.001
jp_i          20.2221    183.043      0.110      0.912    -338.535     378.980
jp_unemp      -3.8768     68.513     -0.057      0.955    -138.160     130.406
n225           0.0342      0.010      3.308      0.001       0.014       0.054
oil           -2.7543      1.154     -2.386      0.017      -5.017      -0.492
usdjpy         3.3189      5.539      0.599      0.549      -7.537      14.175
ar.L1         -0.4625      0.207     -2.229      0.026      -0.869      -0.056
ma.L1          0.6683      0.190      3.514      0.000       0.295       1.041
sigma2      3254.4271    224.249     14.513      0.000    2814.907    3693.947
===================================================================================
Ljung-Box (L1) (Q):                   0.03   Jarque-Bera (JB):               100.90
Prob(Q):                              0.86   Prob(JB):                         0.00
Heteroskedasticity (H):               2.23   Skew:                            -0.67
Prob(H) (two-sided):                  0.00   Kurtosis:                         5.93
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).


print("ARIMAX(1,1,1) / all ")
pred_arimax011_all = predict_from_arima(arimax_all, y_test, test_X=df_test[df_test.columns.difference(["Tokyo Gas"])])
make_plot(y_train, y_test, pred_arimax011_all, "ARIMAX(1,1,1)/all ")
metrics_arimax011_all = calc_metrics(y_test, pred_arimax011_all, return_dict=True)

ARIMAX(1,1,1) / all

Test Error Metrics
MAE: 77.2154
MSE: 10671.9102
MAPE: 0.0388
sMAPE: 0.0375
MASE: -0.6512


fig, ax = plt.subplots(figsize=(16,6))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
pred_arimax011_all.plot(ax=ax, label="ARIMAX(1,1,1)/all exor", linestyle="dashed", color = 'red')
pred_arimax011_oil.plot(ax=ax, label="ARIMAX(1,1,1)/oil", linestyle="dashed")
pred_arimax011_n225.plot(ax=ax, label="ARIMAX(1,1,1)/n225", linestyle="dashed" )
plt.legend()
plt.show()


#Accuracy Check
weekly_pred = dict()
weekly_metrics = dict()

weekly_pred["ARIMA(0,1,1) / No-"] = pred_arima011
weekly_metrics["ARIMA(0,1,1) / No-"] = metrics_arima011

weekly_pred["ARIMAX(0,1,1) / all"] = pred_arimax011_all
weekly_metrics["ARIMAX(0,1,1) / all"] = metrics_arimax011_all

weekly_pred["ARIMAX(0,1,1) / n225"] = pred_arimax011_n225
weekly_metrics["ARIMAX(0,1,1) / n225"] = metrics_arimax011_n225

weekly_pred["ARIMAX(0,1,1) / oil"] = pred_arimax011_oil
weekly_metrics["ARIMAX(0,1,1) / oil "] = metrics_arimax011_oil

pd.DataFrame(weekly_metrics).T


tokyo = main5.loc[main5["Name"]=="Tokyo Gas", "Adjusted Close"]
tokyo = tokyo.dropna()
tokyo.name = "tokyo"


tokyo = pd.DataFrame(tokyo)
tokyo.reset_index()


# Check stationarity
create_plot_adf_kpss(tokyo, "Tokyo_original")

ADF/KPSS tests for Tokyo_original (alpha=0.05):
stationarity from ADF test: False
stationarity from KPSS test('c'): False
stationarity from KPSS test('ct'): False


# Take first difference
tokyo_diff = tokyo.diff().dropna()


# Check stationarity
create_plot_adf_kpss(tokyo_diff, "Tokyo (diff(1))")

ADF/KPSS tests for Tokyo (diff(1)) (alpha=0.05):
stationarity from ADF test: True
stationarity from KPSS test('c'): True
stationarity from KPSS test('ct'): True


# Using data before 2020 as training
y_train = tokyo[tokyo.index.year!=2021]
y_test = tokyo[tokyo.index.year==2021]


y_train


# Merge data and fill NAs with interpolation
tokyo_1 = pd.concat([tokyo, oil_s], axis=1)
tokyo_1 = tokyo_1.dropna(subset=["tokyo"])
tokyo_1["oil"] = tokyo_1["oil"].interpolate()
tokyo_1


# Take first difference
tokyo_1_diff = tokyo_1.diff().dropna()


# Split into train/test
train_diff1 = tokyo_1_diff[tokyo_1_diff.index.year!=2021]
test_diff1 = tokyo_1_diff[tokyo_1_diff.index.year==2021]


from statsmodels.tsa.vector_ar.var_model import VAR
var_model1 = VAR(train_diff1)

results_aic1 =[]
for p in range(1,21):
    results1 = var_model1.fit(p)
    results_aic1.append(results1.aic)


# Min=2
plt.plot(list(np.arange(1,21,1)), results_aic1, marker="o")
plt.xlabel("Order")
plt.ylabel("AIC")
plt.show()


var2_model1 = var_model1.fit(6)
print(var2_model1.summary())

  Summary of Regression Results   
==================================
Model:                         VAR
Method:                        OLS
Date:           Thu, 02, Jun, 2022
Time:                     20:54:00
--------------------------------------------------------------------
No. of Equations:         2.00000    BIC:                    9.25338
Nobs:                     968.000    HQIC:                   9.17228
Log likelihood:          -7136.32    FPE:                    9158.52
AIC:                      9.12244    Det(Omega_mle):         8917.39
--------------------------------------------------------------------
Results for equation tokyo
===========================================================================
              coefficient       std. error           t-stat            prob
---------------------------------------------------------------------------
const           -0.340061         1.246938           -0.273           0.785
L1.tokyo         0.022771         0.032311            0.705           0.481
L1.oil          -0.386131         0.513725           -0.752           0.452
L2.tokyo        -0.049426         0.032070           -1.541           0.123
L2.oil          -0.638941         0.553575           -1.154           0.248
L3.tokyo        -0.083926         0.032066           -2.617           0.009
L3.oil          -0.648369         0.562825           -1.152           0.249
L4.tokyo        -0.080839         0.032012           -2.525           0.012
L4.oil           0.452125         0.562477            0.804           0.422
L5.tokyo         0.102002         0.032073            3.180           0.001
L5.oil           0.862463         0.553982            1.557           0.120
L6.tokyo        -0.036055         0.032241           -1.118           0.263
L6.oil          -0.443726         0.514118           -0.863           0.388
===========================================================================

Results for equation oil
===========================================================================
              coefficient       std. error           t-stat            prob
---------------------------------------------------------------------------
const           -0.009125         0.078336           -0.116           0.907
L1.tokyo        -0.001432         0.002030           -0.705           0.481
L1.oil          -0.401247         0.032273          -12.433           0.000
L2.tokyo         0.002468         0.002015            1.225           0.221
L2.oil          -0.199741         0.034777           -5.743           0.000
L3.tokyo        -0.002999         0.002014           -1.489           0.137
L3.oil          -0.095167         0.035358           -2.692           0.007
L4.tokyo        -0.000974         0.002011           -0.484           0.628
L4.oil          -0.040897         0.035336           -1.157           0.247
L5.tokyo         0.000810         0.002015            0.402           0.688
L5.oil           0.026968         0.034802            0.775           0.438
L6.tokyo        -0.002688         0.002025           -1.327           0.185
L6.oil           0.069058         0.032298            2.138           0.033
===========================================================================

Correlation matrix of residuals
            tokyo       oil
tokyo    1.000000  0.035334
oil      0.035334  1.000000


# Calculate yhat
yhat_var2_1 = var2_model1.forecast(var_model1.endog, steps=len(test_diff1))


# clean up yhat
df_yhat_var2_1 = pd.DataFrame(yhat_var2_1)
df_yhat_var2_1.index = test_diff1.index
df_yhat_var2_1.columns = test_diff1.columns
df_yhat_var2_1


# Recover first order differencing
df_pred_var2_1 = pd.concat([tokyo_1[tokyo_1.index==pd.datetime(2020,12,30)], df_yhat_var2_1], axis=0).cumsum()
df_pred_var2_1 = df_pred_var2_1[df_pred_var2_1.index!=pd.datetime(2020,12,30)]


y_pred_var2_1 = df_pred_var2_1["tokyo"]


fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_var2_1.plot(ax=ax, label="VAR(6) with Oil Price", linestyle="dashed")
plt.legend()
plt.show()


var2_metrics1 = calc_metrics(y_test, y_pred_var2_1, return_dict=True)

Test Error Metrics
MAE: 173.6549
MSE: 42873.2797
MAPE: 0.0833
sMAPE: 0.0786
MASE: tokyo   -7.4615
dtype: float64


# Merge data and fill NAs with interpolation
tokyo_2 = pd.concat([tokyo, oil_s, n225_s], axis=1)
tokyo_2 = tokyo_2.dropna(subset=["tokyo"])
tokyo_2["oil"] = tokyo_2["oil"].interpolate()
tokyo_2["n225"] = tokyo_2["n225"].interpolate()
tokyo_2


# Take first difference
tokyo_2_diff = tokyo_2.diff().dropna()


# Split into train/test
train_diff2 = tokyo_2_diff[tokyo_2_diff.index.year!=2021]
test_diff2 = tokyo_2_diff[tokyo_2_diff.index.year==2021]


from statsmodels.tsa.vector_ar.var_model import VAR
var_model2 = VAR(train_diff2)

results_aic2 =[]
for p in range(1,21):
    results2 = var_model2.fit(p)
    results_aic2.append(results2.aic)


# Min=2
plt.plot(list(np.arange(1,21,1)), results_aic2, marker="o")
plt.xlabel("Order")
plt.ylabel("AIC")
plt.show()


var2_model2 = var_model2.fit(20)
print(var2_model2.summary())

  Summary of Regression Results   
==================================
Model:                         VAR
Method:                        OLS
Date:           Wed, 01, Jun, 2022
Time:                     18:34:47
--------------------------------------------------------------------
No. of Equations:         3.00000    BIC:                    20.8181
Nobs:                     954.000    HQIC:                   20.2408
Log likelihood:          -13363.5    FPE:                4.32974e+08
AIC:                      19.8857    Det(Omega_mle):     3.59509e+08
--------------------------------------------------------------------
Results for equation tokyo
============================================================================
               coefficient       std. error           t-stat            prob
----------------------------------------------------------------------------
const             0.351132         1.258189            0.279           0.780
L1.tokyo          0.015093         0.036327            0.415           0.678
L1.oil           -0.542846         0.558643           -0.972           0.331
L1.n225          -0.002542         0.005798           -0.438           0.661
L2.tokyo         -0.064720         0.036285           -1.784           0.074
L2.oil           -0.454756         0.602104           -0.755           0.450
L2.n225           0.002616         0.005812            0.450           0.653
L3.tokyo         -0.100397         0.036229           -2.771           0.006
L3.oil           -0.015104         0.612118           -0.025           0.980
L3.n225           0.006219         0.005833            1.066           0.286
L4.tokyo         -0.095096         0.036387           -2.613           0.009
L4.oil            0.948821         0.615096            1.543           0.123
L4.n225           0.002262         0.005842            0.387           0.699
L5.tokyo          0.098587         0.036411            2.708           0.007
L5.oil            1.129825         0.616268            1.833           0.067
L5.n225          -0.003429         0.005845           -0.587           0.557
L6.tokyo         -0.081797         0.036388           -2.248           0.025
L6.oil           -0.062030         0.615274           -0.101           0.920
L6.n225           0.006804         0.005881            1.157           0.247
L7.tokyo          0.032459         0.036406            0.892           0.373
L7.oil            0.680964         0.614076            1.109           0.267
L7.n225          -0.008665         0.005890           -1.471           0.141
L8.tokyo         -0.037013         0.036476           -1.015           0.310
L8.oil           -0.436675         0.615356           -0.710           0.478
L8.n225          -0.013087         0.005909           -2.215           0.027
L9.tokyo         -0.031780         0.036575           -0.869           0.385
L9.oil            0.414432         0.611860            0.677           0.498
L9.n225          -0.009782         0.005930           -1.650           0.099
L10.tokyo        -0.002452         0.036424           -0.067           0.946
L10.oil           0.401559         0.605260            0.663           0.507
L10.n225         -0.003027         0.005930           -0.510           0.610
L11.tokyo         0.056379         0.036410            1.548           0.122
L11.oil          -0.146303         0.605980           -0.241           0.809
L11.n225         -0.009915         0.005935           -1.671           0.095
L12.tokyo        -0.034663         0.036572           -0.948           0.343
L12.oil          -0.611684         0.608674           -1.005           0.315
L12.n225          0.004667         0.005926            0.788           0.431
L13.tokyo        -0.006824         0.036293           -0.188           0.851
L13.oil          -0.758233         0.610644           -1.242           0.214
L13.n225         -0.002400         0.005905           -0.406           0.684
L14.tokyo         0.067055         0.036180            1.853           0.064
L14.oil          -0.238576         0.610996           -0.390           0.696
L14.n225         -0.019122         0.005881           -3.251           0.001
L15.tokyo         0.092803         0.036178            2.565           0.010
L15.oil           0.437240         0.609467            0.717           0.473
L15.n225         -0.020689         0.005889           -3.513           0.000
L16.tokyo        -0.083095         0.036116           -2.301           0.021
L16.oil           1.153692         0.602314            1.915           0.055
L16.n225          0.008427         0.005931            1.421           0.155
L17.tokyo        -0.027478         0.036371           -0.755           0.450
L17.oil           0.386530         0.601252            0.643           0.520
L17.n225         -0.004870         0.005923           -0.822           0.411
L18.tokyo        -0.027572         0.036377           -0.758           0.448
L18.oil           0.089415         0.595950            0.150           0.881
L18.n225          0.009880         0.005925            1.667           0.095
L19.tokyo        -0.039782         0.036341           -1.095           0.274
L19.oil          -0.179430         0.581900           -0.308           0.758
L19.n225          0.009633         0.005934            1.623           0.105
L20.tokyo        -0.021900         0.036689           -0.597           0.551
L20.oil          -0.277037         0.533856           -0.519           0.604
L20.n225         -0.013835         0.005961           -2.321           0.020
============================================================================

Results for equation oil
============================================================================
               coefficient       std. error           t-stat            prob
----------------------------------------------------------------------------
const            -0.048632         0.075640           -0.643           0.520
L1.tokyo          0.000459         0.002184            0.210           0.834
L1.oil           -0.386837         0.033584          -11.518           0.000
L1.n225          -0.000450         0.000349           -1.292           0.196
L2.tokyo          0.000029         0.002181            0.013           0.989
L2.oil           -0.217058         0.036197           -5.997           0.000
L2.n225           0.000973         0.000349            2.785           0.005
L3.tokyo         -0.003587         0.002178           -1.647           0.100
L3.oil           -0.121988         0.036799           -3.315           0.001
L3.n225           0.000523         0.000351            1.492           0.136
L4.tokyo         -0.002255         0.002187           -1.031           0.303
L4.oil           -0.067169         0.036978           -1.816           0.069
L4.n225           0.000081         0.000351            0.231           0.818
L5.tokyo         -0.002069         0.002189           -0.945           0.345
L5.oil           -0.006405         0.037049           -0.173           0.863
L5.n225           0.001268         0.000351            3.608           0.000
L6.tokyo         -0.003590         0.002188           -1.641           0.101
L6.oil            0.055456         0.036989            1.499           0.134
L6.n225           0.000682         0.000354            1.929           0.054
L7.tokyo          0.000231         0.002189            0.105           0.916
L7.oil           -0.000465         0.036917           -0.013           0.990
L7.n225           0.000733         0.000354            2.071           0.038
L8.tokyo         -0.003090         0.002193           -1.409           0.159
L8.oil           -0.014258         0.036994           -0.385           0.700
L8.n225           0.000437         0.000355            1.229           0.219
L9.tokyo          0.001118         0.002199            0.509           0.611
L9.oil           -0.004411         0.036784           -0.120           0.905
L9.n225           0.000171         0.000357            0.478           0.632
L10.tokyo         0.000171         0.002190            0.078           0.938
L10.oil          -0.055680         0.036387           -1.530           0.126
L10.n225         -0.000211         0.000356           -0.592           0.554
L11.tokyo        -0.005921         0.002189           -2.705           0.007
L11.oil          -0.088633         0.036430           -2.433           0.015
L11.n225          0.000960         0.000357            2.689           0.007
L12.tokyo        -0.000430         0.002199           -0.196           0.845
L12.oil          -0.085505         0.036592           -2.337           0.019
L12.n225          0.000291         0.000356            0.817           0.414
L13.tokyo         0.000204         0.002182            0.094           0.925
L13.oil           0.019311         0.036711            0.526           0.599
L13.n225          0.000809         0.000355            2.278           0.023
L14.tokyo         0.000654         0.002175            0.300           0.764
L14.oil          -0.014291         0.036732           -0.389           0.697
L14.n225         -0.000225         0.000354           -0.636           0.525
L15.tokyo        -0.002266         0.002175           -1.042           0.298
L15.oil           0.026914         0.036640            0.735           0.463
L15.n225         -0.000203         0.000354           -0.574           0.566
L16.tokyo        -0.008418         0.002171           -3.877           0.000
L16.oil           0.066019         0.036210            1.823           0.068
L16.n225         -0.000112         0.000357           -0.314           0.754
L17.tokyo         0.005917         0.002187            2.706           0.007
L17.oil           0.010854         0.036146            0.300           0.764
L17.n225          0.000643         0.000356            1.804           0.071
L18.tokyo        -0.003321         0.002187           -1.518           0.129
L18.oil          -0.012463         0.035827           -0.348           0.728
L18.n225         -0.001677         0.000356           -4.709           0.000
L19.tokyo         0.008701         0.002185            3.983           0.000
L19.oil          -0.008770         0.034983           -0.251           0.802
L19.n225         -0.001238         0.000357           -3.470           0.001
L20.tokyo         0.000461         0.002206            0.209           0.834
L20.oil           0.039802         0.032094            1.240           0.215
L20.n225          0.000699         0.000358            1.950           0.051
============================================================================

Results for equation n225
============================================================================
               coefficient       std. error           t-stat            prob
----------------------------------------------------------------------------
const            10.241918         7.960552            1.287           0.198
L1.tokyo          0.017281         0.229838            0.075           0.940
L1.oil           12.224234         3.534529            3.459           0.001
L1.n225          -0.011759         0.036685           -0.321           0.749
L2.tokyo         -0.317532         0.229574           -1.383           0.167
L2.oil           13.104383         3.809508            3.440           0.001
L2.n225           0.075546         0.036772            2.054           0.040
L3.tokyo         -0.529180         0.229219           -2.309           0.021
L3.oil            7.733229         3.872866            1.997           0.046
L3.n225           0.036308         0.036905            0.984           0.325
L4.tokyo         -0.134185         0.230217           -0.583           0.560
L4.oil            9.623173         3.891711            2.473           0.013
L4.n225           0.050597         0.036965            1.369           0.171
L5.tokyo          0.204385         0.230373            0.887           0.375
L5.oil            1.819025         3.899121            0.467           0.641
L5.n225          -0.025090         0.036983           -0.678           0.497
L6.tokyo         -0.273477         0.230225           -1.188           0.235
L6.oil            0.825211         3.892837            0.212           0.832
L6.n225          -0.030005         0.037211           -0.806           0.420
L7.tokyo          0.625427         0.230339            2.715           0.007
L7.oil           -7.693255         3.885257           -1.980           0.048
L7.n225          -0.087963         0.037267           -2.360           0.018
L8.tokyo          0.136385         0.230784            0.591           0.555
L8.oil            5.373894         3.893356            1.380           0.168
L8.n225          -0.065004         0.037389           -1.739           0.082
L9.tokyo          0.150621         0.231409            0.651           0.515
L9.oil            7.570115         3.871231            1.955           0.051
L9.n225           0.019005         0.037519            0.507           0.612
L10.tokyo        -0.152613         0.230453           -0.662           0.508
L10.oil          -2.203638         3.829478           -0.575           0.565
L10.n225          0.055288         0.037517            1.474           0.141
L11.tokyo         0.384781         0.230368            1.670           0.095
L11.oil          -6.074745         3.834033           -1.584           0.113
L11.n225         -0.041679         0.037551           -1.110           0.267
L12.tokyo         0.050651         0.231393            0.219           0.827
L12.oil          -0.564994         3.851079           -0.147           0.883
L12.n225          0.014717         0.037495            0.393           0.695
L13.tokyo         0.051655         0.229626            0.225           0.822
L13.oil           2.866915         3.863538            0.742           0.458
L13.n225          0.032218         0.037362            0.862           0.389
L14.tokyo         0.571922         0.228911            2.498           0.012
L14.oil           6.297827         3.865770            1.629           0.103
L14.n225         -0.062885         0.037209           -1.690           0.091
L15.tokyo         0.236120         0.228899            1.032           0.302
L15.oil           6.555963         3.856092            1.700           0.089
L15.n225         -0.034248         0.037259           -0.919           0.358
L16.tokyo        -0.272733         0.228503           -1.194           0.233
L16.oil           6.579832         3.810839            1.727           0.084
L16.n225         -0.014039         0.037527           -0.374           0.708
L17.tokyo         0.040175         0.230119            0.175           0.861
L17.oil           1.508583         3.804118            0.397           0.692
L17.n225          0.000349         0.037474            0.009           0.993
L18.tokyo        -0.453015         0.230155           -1.968           0.049
L18.oil          -3.018696         3.770569           -0.801           0.423
L18.n225          0.010712         0.037487            0.286           0.775
L19.tokyo        -0.334998         0.229927           -1.457           0.145
L19.oil          -3.806185         3.681677           -1.034           0.301
L19.n225          0.034964         0.037545            0.931           0.352
L20.tokyo         0.217767         0.232130            0.938           0.348
L20.oil           1.949594         3.377705            0.577           0.564
L20.n225         -0.062460         0.037718           -1.656           0.098
============================================================================

Correlation matrix of residuals
            tokyo       oil      n225
tokyo    1.000000  0.071436  0.401044
oil      0.071436  1.000000  0.121275
n225     0.401044  0.121275  1.000000


# Calculate yhat
yhat_var2_2 = var2_model2.forecast(var_model2.endog, steps=len(test_diff2))


# clean up yhat
df_yhat_var2_2 = pd.DataFrame(yhat_var2_2)
df_yhat_var2_2.index = test_diff2.index
df_yhat_var2_2.columns = test_diff2.columns
df_yhat_var2_2


# Recover first order differencing
df_pred_var2_2 = pd.concat([tokyo_2[tokyo_2.index==pd.datetime(2020,12,30)], df_yhat_var2_2], axis=0).cumsum()
df_pred_var2_2 = df_pred_var2_2[df_pred_var2_2.index!=pd.datetime(2020,12,30)]


y_pred_var2_2 = df_pred_var2_2["tokyo"]


fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_var2_2.plot(ax=ax, label="VAR(20) with Oil Price & Nikkei225", linestyle="dashed")
plt.legend()
plt.show()


var2_metrics2 = calc_metrics(y_test, y_pred_var2_2, return_dict=True)

Test Error Metrics
MAE: 164.9285
MSE: 40503.7034
MAPE: 0.0793
sMAPE: 0.0749
MASE: -7.0866


# Merge data and fill NAs with interpolation
tokyo_3 = pd.concat([tokyo, oil_s, n225_s, unemp_s], axis=1)
tokyo_3["jp_unemp"] = tokyo_3["jp_unemp"].fillna(method="ffill")
tokyo_3 = tokyo_3.dropna(subset=["tokyo"])
tokyo_3["oil"] = tokyo_3["oil"].interpolate()
tokyo_3["n225"] = tokyo_3["n225"].interpolate()
tokyo_3[tokyo_3.isnull().any(axis=1)]


# Take first difference
tokyo_3_diff = tokyo_3.diff().dropna()


# Split into train/test
train_diff3 = tokyo_3_diff[tokyo_3_diff.index.year!=2021]
test_diff3 = tokyo_3_diff[tokyo_3_diff.index.year==2021]


from statsmodels.tsa.vector_ar.var_model import VAR
var_model3 = VAR(train_diff3)

results_aic3 =[]
for p in range(1,21):
    results3 = var_model3.fit(p)
    results_aic3.append(results3.aic)


# Min=2
plt.plot(list(np.arange(1,21,1)), results_aic3, marker="o")
plt.xlabel("Order")
plt.ylabel("AIC")
plt.show()


var2_model3 = var_model3.fit(2)
print(var2_model3.summary())

  Summary of Regression Results   
==================================
Model:                         VAR
Method:                        OLS
Date:           Wed, 01, Jun, 2022
Time:                     11:41:01
--------------------------------------------------------------------
No. of Equations:         4.00000    BIC:                    13.1836
Nobs:                     972.000    HQIC:                   13.0717
Log likelihood:          -11800.2    FPE:                    443700.
AIC:                      13.0029    Det(Omega_mle):         427641.
--------------------------------------------------------------------
Results for equation tokyo
==============================================================================
                 coefficient       std. error           t-stat            prob
------------------------------------------------------------------------------
const              -0.375938         1.265658           -0.297           0.766
L1.tokyo            0.016420         0.035015            0.469           0.639
L1.oil             -0.335657         0.514277           -0.653           0.514
L1.n225             0.000997         0.005647            0.176           0.860
L1.jp_unemp       -10.421555        41.499732           -0.251           0.802
L2.tokyo           -0.061461         0.035011           -1.756           0.079
L2.oil             -0.502852         0.513760           -0.979           0.328
L2.n225             0.003756         0.005655            0.664           0.507
L2.jp_unemp        25.282122        41.490865            0.609           0.542
==============================================================================

Results for equation oil
==============================================================================
                 coefficient       std. error           t-stat            prob
------------------------------------------------------------------------------
const              -0.009462         0.078454           -0.121           0.904
L1.tokyo            0.000509         0.002170            0.235           0.815
L1.oil             -0.377779         0.031878          -11.851           0.000
L1.n225            -0.000589         0.000350           -1.683           0.092
L1.jp_unemp         0.138423         2.572431            0.054           0.957
L2.tokyo            0.000794         0.002170            0.366           0.715
L2.oil             -0.160489         0.031846           -5.039           0.000
L2.n225             0.000744         0.000351            2.122           0.034
L2.jp_unemp         0.569405         2.571881            0.221           0.825
==============================================================================

Results for equation n225
==============================================================================
                 coefficient       std. error           t-stat            prob
------------------------------------------------------------------------------
const               7.362547         7.836165            0.940           0.347
L1.tokyo           -0.122056         0.216791           -0.563           0.573
L1.oil              9.626528         3.184081            3.023           0.003
L1.n225             0.017272         0.034963            0.494           0.621
L1.jp_unemp        70.749315       256.940443            0.275           0.783
L2.tokyo           -0.396456         0.216764           -1.829           0.067
L2.oil             10.037418         3.180882            3.156           0.002
L2.n225             0.086823         0.035013            2.480           0.013
L2.jp_unemp       -34.260254       256.885540           -0.133           0.894
==============================================================================

Results for equation jp_unemp
==============================================================================
                 coefficient       std. error           t-stat            prob
------------------------------------------------------------------------------
const               0.000131         0.000987            0.132           0.895
L1.tokyo           -0.000003         0.000027           -0.095           0.925
L1.oil              0.000297         0.000401            0.742           0.458
L1.n225             0.000001         0.000004            0.145           0.885
L1.jp_unemp         0.000608         0.032353            0.019           0.985
L2.tokyo            0.000003         0.000027            0.121           0.904
L2.oil              0.000070         0.000401            0.176           0.860
L2.n225            -0.000004         0.000004           -0.916           0.360
L2.jp_unemp        -0.002637         0.032346           -0.082           0.935
==============================================================================

Correlation matrix of residuals
               tokyo       oil      n225  jp_unemp
tokyo       1.000000  0.045149  0.399272 -0.068800
oil         0.045149  1.000000  0.110902 -0.004741
n225        0.399272  0.110902  1.000000 -0.085350
jp_unemp   -0.068800 -0.004741 -0.085350  1.000000


# Calculate yhat
yhat_var2_3 = var2_model3.forecast(var_model3.endog, steps=len(test_diff3))


# clean up yhat
df_yhat_var2_3 = pd.DataFrame(yhat_var2_3)
df_yhat_var2_3.index = test_diff3.index
df_yhat_var2_3.columns = test_diff3.columns
df_yhat_var2_3


# Recover first order differencing
df_pred_var2_3 = pd.concat([tokyo_3[tokyo_3.index==pd.datetime(2020,12,30)], df_yhat_var2_3], axis=0).cumsum()
df_pred_var2_3 = df_pred_var2_3[df_pred_var2_3.index!=pd.datetime(2020,12,30)]

y_pred_var2_3 = df_pred_var2_3["tokyo"]


fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_var2_3.plot(ax=ax, label="VAR(2) with Oil, N225, Unemployement", linestyle="dashed")
plt.legend()
plt.show()


var2_metrics3 = calc_metrics(y_test, y_pred_var2_3, return_dict=True)

Test Error Metrics
MAE: 179.2476
MSE: 44981.3307
MAPE: 0.0859
sMAPE: 0.081
MASE: -7.7018


# Merge data and fill NAs with interpolation
tokyo_4 = pd.concat([tokyo, oil_s, n225_s, unemp_s, gdp_s], axis=1)
tokyo_4["jp_gdp"] = tokyo_4["jp_gdp"].fillna(method="ffill")
tokyo_4["jp_unemp"] = tokyo_4["jp_unemp"].fillna(method="ffill")
tokyo_4 = tokyo_4.dropna(subset=["tokyo"])
tokyo_4["oil"] = tokyo_4["oil"].interpolate()
tokyo_4["n225"] = tokyo_4["n225"].interpolate()
tokyo_4[tokyo_4.isnull().any(axis=1)]


# Take first difference
tokyo_4_diff = tokyo_4.diff().dropna()


# Split into train/test
train_diff4 = tokyo_4_diff[tokyo_4_diff.index.year!=2021]
test_diff4 = tokyo_4_diff[tokyo_4_diff.index.year==2021]


from statsmodels.tsa.vector_ar.var_model import VAR
var_model4 = VAR(train_diff4)


results_aic4 =[]
for p in range(1,21):
    results4 = var_model4.fit(p)
    results_aic4.append(results4.aic)


# Min=2
plt.plot(list(np.arange(1,21,1)), results_aic4, marker="o")
plt.xlabel("Order")
plt.ylabel("AIC")
plt.show()


var2_model4 = var_model4.fit(14)
print(var2_model4.summary())

  Summary of Regression Results   
==================================
Model:                         VAR
Method:                        OLS
Date:           Wed, 01, Jun, 2022
Time:                     11:42:13
--------------------------------------------------------------------
No. of Equations:         5.00000    BIC:                    29.2735
Nobs:                     960.000    HQIC:                   28.1591
Log likelihood:          -19643.3    FPE:                8.55638e+11
AIC:                      27.4738    Det(Omega_mle):     5.98898e+11
--------------------------------------------------------------------
Results for equation tokyo
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const                0.129350         1.274157            0.102           0.919
L1.tokyo             0.016725         0.036604            0.457           0.648
L1.oil              -0.028633         0.681797           -0.042           0.967
L1.n225             -0.001105         0.006018           -0.184           0.854
L1.jp_unemp        -24.229457        41.519050           -0.584           0.560
L1.jp_gdp            0.000133         0.000812            0.164           0.870
L2.tokyo            -0.064869         0.036636           -1.771           0.077
L2.oil              -0.166729         0.632665           -0.264           0.792
L2.n225              0.001822         0.006011            0.303           0.762
L2.jp_unemp         23.692796        41.522631            0.571           0.568
L2.jp_gdp           -0.000444         0.000812           -0.547           0.584
L3.tokyo            -0.100375         0.036697           -2.735           0.006
L3.oil              -0.034243         0.629711           -0.054           0.957
L3.n225              0.005857         0.006025            0.972           0.331
L3.jp_unemp         17.504739        41.536050            0.421           0.673
L3.jp_gdp           -0.000317         0.000813           -0.390           0.696
L4.tokyo            -0.097246         0.037056           -2.624           0.009
L4.oil               0.724615         0.622571            1.164           0.244
L4.n225              0.002353         0.006005            0.392           0.695
L4.jp_unemp        -21.802086        41.532733           -0.525           0.600
L4.jp_gdp           -0.000432         0.000808           -0.535           0.593
L5.tokyo             0.102288         0.037213            2.749           0.006
L5.oil               1.270442         0.622807            2.040           0.041
L5.n225             -0.006042         0.006038           -1.001           0.317
L5.jp_unemp         37.396623        41.507433            0.901           0.368
L5.jp_gdp           -0.000901         0.000806           -1.119           0.263
L6.tokyo            -0.068382         0.037412           -1.828           0.068
L6.oil               0.113524         0.618843            0.183           0.854
L6.n225              0.005998         0.006059            0.990           0.322
L6.jp_unemp        -36.427521        41.432628           -0.879           0.379
L6.jp_gdp            0.000494         0.000803            0.615           0.539
L7.tokyo             0.023498         0.037564            0.626           0.532
L7.oil               0.729607         0.618033            1.181           0.238
L7.n225             -0.008081         0.006181           -1.307           0.191
L7.jp_unemp         -9.059245        41.379854           -0.219           0.827
L7.jp_gdp           -0.000706         0.000800           -0.882           0.378
L8.tokyo            -0.044606         0.037493           -1.190           0.234
L8.oil              -0.440661         0.621036           -0.710           0.478
L8.n225             -0.012703         0.006157           -2.063           0.039
L8.jp_unemp         12.313401        41.334176            0.298           0.766
L8.jp_gdp            0.000970         0.000798            1.215           0.225
L9.tokyo            -0.026675         0.037550           -0.710           0.477
L9.oil               0.270166         0.622797            0.434           0.664
L9.n225             -0.011323         0.006185           -1.831           0.067
L9.jp_unemp        -11.739830        41.321732           -0.284           0.776
L9.jp_gdp           -0.000996         0.000787           -1.266           0.206
L10.tokyo            0.004736         0.037470            0.126           0.899
L10.oil              0.264198         0.621966            0.425           0.671
L10.n225            -0.005669         0.006173           -0.918           0.358
L10.jp_unemp       -10.212822        41.318051           -0.247           0.805
L10.jp_gdp          -0.000348         0.000776           -0.448           0.654
L11.tokyo            0.068734         0.037471            1.834           0.067
L11.oil              0.074409         0.621755            0.120           0.905
L11.n225            -0.013184         0.006130           -2.151           0.032
L11.jp_unemp        24.897222        41.300049            0.603           0.547
L11.jp_gdp          -0.000003         0.000773           -0.004           0.997
L12.tokyo           -0.044714         0.037785           -1.183           0.237
L12.oil             -0.630755         0.617852           -1.021           0.307
L12.n225             0.004000         0.006187            0.646           0.518
L12.jp_unemp        -0.336486        41.272195           -0.008           0.993
L12.jp_gdp          -0.000149         0.000763           -0.195           0.845
L13.tokyo            0.004004         0.037722            0.106           0.915
L13.oil             -0.634105         0.603397           -1.051           0.293
L13.n225            -0.001136         0.006118           -0.186           0.853
L13.jp_unemp        13.934867        41.276969            0.338           0.736
L13.jp_gdp          -0.000178         0.000768           -0.232           0.817
L14.tokyo            0.046033         0.037786            1.218           0.223
L14.oil             -0.058939         0.551484           -0.107           0.915
L14.n225            -0.015614         0.006122           -2.550           0.011
L14.jp_unemp         7.741784        41.634133            0.186           0.852
L14.jp_gdp          -0.000784         0.000947           -0.827           0.408
===============================================================================

Results for equation oil
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const               -0.052044         0.059769           -0.871           0.384
L1.tokyo            -0.000988         0.001717           -0.576           0.565
L1.oil              -0.240821         0.031982           -7.530           0.000
L1.n225             -0.000111         0.000282           -0.392           0.695
L1.jp_unemp          0.769826         1.947607            0.395           0.693
L1.jp_gdp           -0.000057         0.000038           -1.487           0.137
L2.tokyo             0.001465         0.001719            0.852           0.394
L2.oil              -0.157049         0.029678           -5.292           0.000
L2.n225              0.000646         0.000282            2.290           0.022
L2.jp_unemp          0.968968         1.947775            0.497           0.619
L2.jp_gdp           -0.000056         0.000038           -1.482           0.138
L3.tokyo            -0.003142         0.001721           -1.825           0.068
L3.oil              -0.099236         0.029539           -3.359           0.001
L3.n225              0.000310         0.000283            1.098           0.272
L3.jp_unemp         -1.003686         1.948405           -0.515           0.606
L3.jp_gdp            0.000002         0.000038            0.045           0.964
L4.tokyo            -0.000407         0.001738           -0.234           0.815
L4.oil              -0.070118         0.029204           -2.401           0.016
L4.n225              0.000518         0.000282            1.838           0.066
L4.jp_unemp         -0.504780         1.948249           -0.259           0.796
L4.jp_gdp            0.000045         0.000038            1.176           0.240
L5.tokyo            -0.002722         0.001746           -1.559           0.119
L5.oil               0.012806         0.029215            0.438           0.661
L5.n225              0.000586         0.000283            2.068           0.039
L5.jp_unemp         -0.924974         1.947062           -0.475           0.635
L5.jp_gdp            0.000018         0.000038            0.464           0.643
L6.tokyo            -0.001736         0.001755           -0.989           0.322
L6.oil               0.024871         0.029029            0.857           0.392
L6.n225              0.000637         0.000284            2.241           0.025
L6.jp_unemp         -0.626759         1.943553           -0.322           0.747
L6.jp_gdp            0.000028         0.000038            0.748           0.455
L7.tokyo             0.000804         0.001762            0.456           0.648
L7.oil              -0.015108         0.028991           -0.521           0.602
L7.n225              0.000388         0.000290            1.339           0.181
L7.jp_unemp         -0.665283         1.941078           -0.343           0.732
L7.jp_gdp            0.000062         0.000038            1.648           0.099
L8.tokyo            -0.001468         0.001759           -0.835           0.404
L8.oil              -0.023386         0.029132           -0.803           0.422
L8.n225              0.000547         0.000289            1.895           0.058
L8.jp_unemp          0.366181         1.938935            0.189           0.850
L8.jp_gdp           -0.000006         0.000037           -0.162           0.871
L9.tokyo             0.001288         0.001761            0.731           0.465
L9.oil              -0.025044         0.029215           -0.857           0.391
L9.n225              0.000115         0.000290            0.398           0.691
L9.jp_unemp          0.557026         1.938351            0.287           0.774
L9.jp_gdp            0.000045         0.000037            1.230           0.219
L10.tokyo            0.001121         0.001758            0.638           0.524
L10.oil             -0.047114         0.029176           -1.615           0.106
L10.n225             0.000033         0.000290            0.115           0.908
L10.jp_unemp         1.264083         1.938179            0.652           0.514
L10.jp_gdp           0.000025         0.000036            0.687           0.492
L11.tokyo           -0.005609         0.001758           -3.191           0.001
L11.oil             -0.065137         0.029166           -2.233           0.026
L11.n225             0.000762         0.000288            2.651           0.008
L11.jp_unemp         0.805814         1.937334            0.416           0.677
L11.jp_gdp           0.000008         0.000036            0.210           0.834
L12.tokyo            0.000260         0.001772            0.147           0.883
L12.oil             -0.057158         0.028983           -1.972           0.049
L12.n225             0.000379         0.000290            1.306           0.192
L12.jp_unemp        -1.542192         1.936028           -0.797           0.426
L12.jp_gdp           0.000018         0.000036            0.492           0.623
L13.tokyo            0.000065         0.001769            0.037           0.971
L13.oil              0.001391         0.028305            0.049           0.961
L13.n225             0.000627         0.000287            2.183           0.029
L13.jp_unemp        -7.709431         1.936252           -3.982           0.000
L13.jp_gdp           0.000819         0.000036           22.733           0.000
L14.tokyo           -0.000391         0.001772           -0.221           0.825
L14.oil             -0.021923         0.025869           -0.847           0.397
L14.n225            -0.000162         0.000287           -0.563           0.573
L14.jp_unemp         2.469414         1.953006            1.264           0.206
L14.jp_gdp          -0.000471         0.000044          -10.608           0.000
===============================================================================

Results for equation n225
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const                9.490934         7.853279            1.209           0.227
L1.tokyo             0.035177         0.225609            0.156           0.876
L1.oil              13.358701         4.202263            3.179           0.001
L1.n225              0.002026         0.037092            0.055           0.956
L1.jp_unemp         15.889881       255.903108            0.062           0.950
L1.jp_gdp            0.004039         0.005003            0.807           0.419
L2.tokyo            -0.360740         0.225807           -1.598           0.110
L2.oil              14.074785         3.899437            3.609           0.000
L2.n225              0.072467         0.037046            1.956           0.050
L2.jp_unemp       -111.736583       255.925179           -0.437           0.662
L2.jp_gdp            0.004443         0.005007            0.887           0.375
L3.tokyo            -0.559796         0.226180           -2.475           0.013
L3.oil               8.233740         3.881231            2.121           0.034
L3.n225              0.033962         0.037132            0.915           0.360
L3.jp_unemp        302.529739       256.007886            1.182           0.237
L3.jp_gdp           -0.006424         0.005012           -1.282           0.200
L4.tokyo            -0.083340         0.228392           -0.365           0.715
L4.oil               7.703406         3.837225            2.008           0.045
L4.n225              0.048352         0.037010            1.306           0.191
L4.jp_unemp         86.194576       255.987439            0.337           0.736
L4.jp_gdp           -0.004920         0.004980           -0.988           0.323
L5.tokyo             0.288460         0.229362            1.258           0.209
L5.oil               1.330679         3.838677            0.347           0.729
L5.n225             -0.037900         0.037214           -1.018           0.308
L5.jp_unemp         72.241820       255.831503            0.282           0.778
L5.jp_gdp           -0.009169         0.004966           -1.846           0.065
L6.tokyo            -0.228389         0.230589           -0.990           0.322
L6.oil               1.133284         3.814248            0.297           0.766
L6.n225             -0.032775         0.037343           -0.878           0.380
L6.jp_unemp       -308.924452       255.370443           -1.210           0.226
L6.jp_gdp            0.004558         0.004950            0.921           0.357
L7.tokyo             0.523991         0.231523            2.263           0.024
L7.oil              -6.176508         3.809251           -1.621           0.105
L7.n225             -0.070185         0.038096           -1.842           0.065
L7.jp_unemp       -167.253858       255.045171           -0.656           0.512
L7.jp_gdp           -0.000452         0.004932           -0.092           0.927
L8.tokyo             0.013497         0.231090            0.058           0.953
L8.oil               6.312837         3.827764            1.649           0.099
L8.n225             -0.061450         0.037951           -1.619           0.105
L8.jp_unemp          1.217440       254.763635            0.005           0.996
L8.jp_gdp            0.011576         0.004920            2.353           0.019
L9.tokyo             0.251338         0.231438            1.086           0.277
L9.oil               6.763598         3.838614            1.762           0.078
L9.n225              0.000676         0.038119            0.018           0.986
L9.jp_unemp       -130.776660       254.686933           -0.513           0.608
L9.jp_gdp           -0.012822         0.004852           -2.643           0.008
L10.tokyo            0.008341         0.230948            0.036           0.971
L10.oil             -3.100924         3.833493           -0.809           0.419
L10.n225             0.017709         0.038049            0.465           0.642
L10.jp_unemp      -212.623498       254.664246           -0.835           0.404
L10.jp_gdp           0.000832         0.004784            0.174           0.862
L11.tokyo            0.544749         0.230951            2.359           0.018
L11.oil             -6.670563         3.832195           -1.741           0.082
L11.n225            -0.053284         0.037784           -1.410           0.158
L11.jp_unemp       167.675546       254.553292            0.659           0.510
L11.jp_gdp           0.002887         0.004765            0.606           0.544
L12.tokyo           -0.171480         0.232889           -0.736           0.462
L12.oil             -0.957744         3.808139           -0.251           0.801
L12.n225             0.028547         0.038131            0.749           0.454
L12.jp_unemp      -219.537466       254.381611           -0.863           0.388
L12.jp_gdp          -0.013040         0.004705           -2.771           0.006
L13.tokyo            0.078293         0.232500            0.337           0.736
L13.oil              1.377585         3.719042            0.370           0.711
L13.n225             0.065810         0.037711            1.745           0.081
L13.jp_unemp        78.291379       254.411038            0.308           0.758
L13.jp_gdp           0.001290         0.004731            0.273           0.785
L14.tokyo            0.330204         0.232894            1.418           0.156
L14.oil              4.007392         3.399076            1.179           0.238
L14.n225            -0.046818         0.037733           -1.241           0.215
L14.jp_unemp       166.025174       256.612424            0.647           0.518
L14.jp_gdp          -0.003510         0.005840           -0.601           0.548
===============================================================================

Results for equation jp_unemp
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const                0.000295         0.001033            0.286           0.775
L1.tokyo             0.000002         0.000030            0.057           0.955
L1.oil               0.000574         0.000553            1.039           0.299
L1.n225             -0.000000         0.000005           -0.005           0.996
L1.jp_unemp         -0.001068         0.033661           -0.032           0.975
L1.jp_gdp            0.000001         0.000001            0.878           0.380
L2.tokyo             0.000008         0.000030            0.262           0.793
L2.oil               0.000452         0.000513            0.882           0.378
L2.n225             -0.000006         0.000005           -1.165           0.244
L2.jp_unemp         -0.003765         0.033664           -0.112           0.911
L2.jp_gdp            0.000000         0.000001            0.164           0.870
L3.tokyo             0.000004         0.000030            0.119           0.906
L3.oil               0.000312         0.000511            0.611           0.541
L3.n225              0.000005         0.000005            0.949           0.343
L3.jp_unemp          0.005519         0.033675            0.164           0.870
L3.jp_gdp           -0.000000         0.000001           -0.007           0.994
L4.tokyo             0.000032         0.000030            1.067           0.286
L4.oil               0.000124         0.000505            0.246           0.805
L4.n225             -0.000006         0.000005           -1.296           0.195
L4.jp_unemp         -0.002105         0.033672           -0.063           0.950
L4.jp_gdp            0.000000         0.000001            0.041           0.968
L5.tokyo            -0.000007         0.000030           -0.245           0.806
L5.oil               0.000160         0.000505            0.317           0.751
L5.n225             -0.000003         0.000005           -0.617           0.537
L5.jp_unemp         -0.003412         0.033652           -0.101           0.919
L5.jp_gdp            0.000000         0.000001            0.027           0.979
L6.tokyo             0.000010         0.000030            0.323           0.747
L6.oil               0.000015         0.000502            0.031           0.975
L6.n225              0.000002         0.000005            0.353           0.724
L6.jp_unemp         -0.004347         0.033591           -0.129           0.897
L6.jp_gdp            0.000000         0.000001            0.717           0.473
L7.tokyo            -0.000036         0.000030           -1.193           0.233
L7.oil               0.000154         0.000501            0.306           0.759
L7.n225              0.000002         0.000005            0.358           0.721
L7.jp_unemp          0.002203         0.033548            0.066           0.948
L7.jp_gdp           -0.000000         0.000001           -0.476           0.634
L8.tokyo            -0.000009         0.000030           -0.297           0.766
L8.oil              -0.001016         0.000504           -2.017           0.044
L8.n225             -0.000002         0.000005           -0.347           0.729
L8.jp_unemp         -0.003088         0.033511           -0.092           0.927
L8.jp_gdp           -0.000000         0.000001           -0.212           0.832
L9.tokyo             0.000040         0.000030            1.326           0.185
L9.oil              -0.000744         0.000505           -1.474           0.140
L9.n225             -0.000003         0.000005           -0.547           0.584
L9.jp_unemp          0.002999         0.033501            0.090           0.929
L9.jp_gdp           -0.000000         0.000001           -0.681           0.496
L10.tokyo            0.000020         0.000030            0.662           0.508
L10.oil             -0.000211         0.000504           -0.417           0.676
L10.n225            -0.000004         0.000005           -0.796           0.426
L10.jp_unemp        -0.000975         0.033498           -0.029           0.977
L10.jp_gdp           0.000000         0.000001            0.067           0.947
L11.tokyo            0.000012         0.000030            0.402           0.687
L11.oil             -0.000256         0.000504           -0.509           0.611
L11.n225             0.000005         0.000005            0.952           0.341
L11.jp_unemp         0.000898         0.033484            0.027           0.979
L11.jp_gdp          -0.000000         0.000001           -0.283           0.777
L12.tokyo           -0.000018         0.000031           -0.597           0.551
L12.oil              0.000068         0.000501            0.135           0.892
L12.n225            -0.000000         0.000005           -0.046           0.963
L12.jp_unemp        -0.005531         0.033461           -0.165           0.869
L12.jp_gdp           0.000000         0.000001            0.094           0.925
L13.tokyo            0.000018         0.000031            0.577           0.564
L13.oil             -0.000156         0.000489           -0.318           0.751
L13.n225            -0.000003         0.000005           -0.659           0.510
L13.jp_unemp        -0.000186         0.033465           -0.006           0.996
L13.jp_gdp           0.000000         0.000001            0.073           0.942
L14.tokyo           -0.000016         0.000031           -0.511           0.610
L14.oil              0.000051         0.000447            0.114           0.909
L14.n225            -0.000008         0.000005           -1.586           0.113
L14.jp_unemp        -0.008884         0.033755           -0.263           0.792
L14.jp_gdp          -0.000001         0.000001           -0.656           0.512
===============================================================================

Results for equation jp_gdp
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const                3.945648        52.752526            0.075           0.940
L1.tokyo             2.901616         1.515475            1.915           0.056
L1.oil             -15.965381        28.227698           -0.566           0.572
L1.n225             -0.007127         0.249159           -0.029           0.977
L1.jp_unemp        278.809583      1718.968052            0.162           0.871
L1.jp_gdp           -0.018299         0.033605           -0.545           0.586
L2.tokyo            -0.696877         1.516803           -0.459           0.646
L2.oil              18.943446        26.193536            0.723           0.470
L2.n225             -0.014815         0.248849           -0.060           0.953
L2.jp_unemp       -154.631785      1719.116307           -0.090           0.928
L2.jp_gdp           -0.012458         0.033631           -0.370           0.711
L3.tokyo            -5.658004         1.519310           -3.724           0.000
L3.oil              47.756189        26.071242            1.832           0.067
L3.n225              0.112994         0.249427            0.453           0.651
L3.jp_unemp       -724.344314      1719.671868           -0.421           0.674
L3.jp_gdp            0.013762         0.033667            0.409           0.683
L4.tokyo             1.801590         1.534169            1.174           0.240
L4.oil              32.903868        25.775641            1.277           0.202
L4.n225              0.556146         0.248608            2.237           0.025
L4.jp_unemp        439.752071      1719.534520            0.256           0.798
L4.jp_gdp            0.028081         0.033450            0.839           0.401
L5.tokyo            -4.275871         1.540684           -2.775           0.006
L5.oil               7.687681        25.785396            0.298           0.766
L5.n225             -1.001938         0.249976           -4.008           0.000
L5.jp_unemp       -567.038507      1718.487058           -0.330           0.741
L5.jp_gdp           -0.003510         0.033361           -0.105           0.916
L6.tokyo             6.041982         1.548923            3.901           0.000
L6.oil              20.777342        25.621299            0.811           0.417
L6.n225             -1.443493         0.250841           -5.755           0.000
L6.jp_unemp       -192.978928      1715.390000           -0.112           0.910
L6.jp_gdp            0.033333         0.033249            1.003           0.316
L7.tokyo             0.988582         1.555202            0.636           0.525
L7.oil              60.062806        25.587733            2.347           0.019
L7.n225             -0.606901         0.255902           -2.372           0.018
L7.jp_unemp         21.416850      1713.205062            0.013           0.990
L7.jp_gdp            0.010253         0.033133            0.309           0.757
L8.tokyo            -4.050084         1.552290           -2.609           0.009
L8.oil              29.208217        25.712089            1.136           0.256
L8.n225              0.163150         0.254929            0.640           0.522
L8.jp_unemp        -12.190116      1711.313912           -0.007           0.994
L8.jp_gdp            0.025064         0.033048            0.758           0.448
L9.tokyo            -1.512220         1.554631           -0.973           0.331
L9.oil              69.581093        25.784974            2.699           0.007
L9.n225              0.257717         0.256055            1.006           0.314
L9.jp_unemp        139.217509      1710.798685            0.081           0.935
L9.jp_gdp           -0.007602         0.032589           -0.233           0.816
L10.tokyo           -2.889163         1.551337           -1.862           0.063
L10.oil             55.784028        25.750575            2.166           0.030
L10.n225             0.086263         0.255587            0.338           0.736
L10.jp_unemp       665.001732      1710.646288            0.389           0.697
L10.jp_gdp          -0.016064         0.032133           -0.500           0.617
L11.tokyo           -2.020448         1.551358           -1.302           0.193
L11.oil             22.373141        25.741855            0.869           0.385
L11.n225             0.826177         0.253803            3.255           0.001
L11.jp_unemp       363.143270      1709.900980            0.212           0.832
L11.jp_gdp          -0.017042         0.032005           -0.532           0.594
L12.tokyo            1.318477         1.564378            0.843           0.399
L12.oil             -0.706699        25.580262           -0.028           0.978
L12.n225             0.204338         0.256138            0.798           0.425
L12.jp_unemp      -139.758907      1708.747753           -0.082           0.935
L12.jp_gdp          -0.037676         0.031606           -1.192           0.233
L13.tokyo            2.182687         1.561763            1.398           0.162
L13.oil            -16.257410        24.981775           -0.651           0.515
L13.n225             0.206257         0.253313            0.814           0.416
L13.jp_unemp       476.176932      1708.945425            0.279           0.781
L13.jp_gdp           0.008251         0.031779            0.260           0.795
L14.tokyo           -1.883682         1.564412           -1.204           0.229
L14.oil              4.666174        22.832482            0.204           0.838
L14.n225            -0.149162         0.253459           -0.589           0.556
L14.jp_unemp      -885.648326      1723.732707           -0.514           0.607
L14.jp_gdp           0.003288         0.039226            0.084           0.933
===============================================================================

Correlation matrix of residuals
               tokyo       oil      n225  jp_unemp    jp_gdp
tokyo       1.000000  0.063808  0.404194 -0.084183  0.010154
oil         0.063808  1.000000  0.161064 -0.007922 -0.000862
n225        0.404194  0.161064  1.000000 -0.082268  0.063166
jp_unemp   -0.084183 -0.007922 -0.082268  1.000000  0.047640
jp_gdp      0.010154 -0.000862  0.063166  0.047640  1.000000


# Calculate yhat
yhat_var2_4 = var2_model4.forecast(var_model4.endog, steps=len(test_diff4))


# clean up yhat
df_yhat_var2_4 = pd.DataFrame(yhat_var2_4)
df_yhat_var2_4.index = test_diff4.index
df_yhat_var2_4.columns = test_diff4.columns
df_yhat_var2_4


# Recover first order differencing
df_pred_var2_4 = pd.concat([tokyo_4[tokyo_4.index==pd.datetime(2020,12,30)], df_yhat_var2_4], axis=0).cumsum()
df_pred_var2_4 = df_pred_var2_4[df_pred_var2_4.index!=pd.datetime(2020,12,30)]

y_pred_var2_4 = df_pred_var2_4["tokyo"]


fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_var2_4.plot(ax=ax, label="VAR(14) with Oil, N225, Unemployement, GDP", linestyle="dashed")
plt.legend()
plt.show()


var2_metrics4 = calc_metrics(y_test, y_pred_var2_4, return_dict=True)

Test Error Metrics
MAE: 155.0108
MSE: 35544.422
MAPE: 0.0744
sMAPE: 0.0706
MASE: -6.6604


# Merge data and fill NAs with interpolation
tokyo_5 = pd.concat([tokyo, oil_s, n225_s, unemp_s, gdp_s, usdjpy_s], axis=1)
tokyo_5["jp_gdp"] = tokyo_5["jp_gdp"].fillna(method="ffill")
tokyo_5["jp_unemp"] = tokyo_5["jp_unemp"].fillna(method="ffill")
tokyo_5 = tokyo_5.dropna(subset=["tokyo"])
tokyo_5["oil"] = tokyo_5["oil"].interpolate()
tokyo_5["n225"] = tokyo_5["n225"].interpolate()
tokyo_5["usdjpy"] = tokyo_5["usdjpy"].interpolate()
tokyo_5[tokyo_5.isnull().any(axis=1)]


# Take first difference
tokyo_5_diff = tokyo_5.diff().dropna()


# Split into train/test
train_diff5 = tokyo_5_diff[tokyo_5_diff.index.year!=2021]
test_diff5 = tokyo_5_diff[tokyo_5_diff.index.year==2021]


from statsmodels.tsa.vector_ar.var_model import VAR
var_model5 = VAR(train_diff5)


results_aic5 =[]
for p in range(1,21):
    results5 = var_model5.fit(p)
    results_aic5.append(results5.aic)


# Min=2
plt.plot(list(np.arange(1,21,1)), results_aic5, marker="o")
plt.xlabel("Order")
plt.ylabel("AIC")
plt.show()


var2_model5 = var_model5.fit(14)
print(var2_model5.summary())

  Summary of Regression Results   
==================================
Model:                         VAR
Method:                        OLS
Date:           Wed, 01, Jun, 2022
Time:                     18:42:17
--------------------------------------------------------------------
No. of Equations:         6.00000    BIC:                    28.6103
Nobs:                     960.000    HQIC:                   27.0094
Log likelihood:          -20155.0    FPE:                2.01203e+11
AIC:                      26.0248    Det(Omega_mle):     1.20938e+11
--------------------------------------------------------------------
Results for equation tokyo
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const                0.462762         1.295484            0.357           0.721
L1.tokyo             0.022950         0.036923            0.622           0.534
L1.oil              -0.007295         0.683806           -0.011           0.991
L1.n225             -0.004750         0.006469           -0.734           0.463
L1.jp_unemp        -24.569380        41.744671           -0.589           0.556
L1.jp_gdp            0.000296         0.000838            0.353           0.724
L1.usdjpy            4.214655         2.785318            1.513           0.130
L2.tokyo            -0.064317         0.036941           -1.741           0.082
L2.oil              -0.031513         0.636530           -0.050           0.961
L2.n225              0.000124         0.006535            0.019           0.985
L2.jp_unemp         17.293702        41.732744            0.414           0.679
L2.jp_gdp           -0.000199         0.000838           -0.237           0.813
L2.usdjpy           -0.485347         2.823843           -0.172           0.864
L3.tokyo            -0.105619         0.036990           -2.855           0.004
L3.oil               0.031918         0.636013            0.050           0.960
L3.n225              0.005300         0.006566            0.807           0.420
L3.jp_unemp         16.948100        41.738858            0.406           0.685
L3.jp_gdp           -0.000352         0.000837           -0.421           0.674
L3.usdjpy            1.477607         2.824899            0.523           0.601
L4.tokyo            -0.084541         0.037415           -2.260           0.024
L4.oil               0.889796         0.627807            1.417           0.156
L4.n225             -0.000916         0.006586           -0.139           0.889
L4.jp_unemp        -12.608159        41.723232           -0.302           0.763
L4.jp_gdp           -0.000584         0.000825           -0.707           0.479
L4.usdjpy            3.644835         2.827963            1.289           0.197
L5.tokyo             0.096493         0.037505            2.573           0.010
L5.oil               1.379520         0.627713            2.198           0.028
L5.n225             -0.003727         0.006631           -0.562           0.574
L5.jp_unemp         29.236720        41.786820            0.700           0.484
L5.jp_gdp           -0.001074         0.000824           -1.304           0.192
L5.usdjpy           -3.479371         2.813602           -1.237           0.216
L6.tokyo            -0.069677         0.037558           -1.855           0.064
L6.oil               0.200759         0.623501            0.322           0.747
L6.n225              0.005802         0.006614            0.877           0.380
L6.jp_unemp        -27.824564        41.796712           -0.666           0.506
L6.jp_gdp            0.000034         0.000822            0.041           0.967
L6.usdjpy            2.577373         2.806375            0.918           0.358
L7.tokyo             0.024201         0.037673            0.642           0.521
L7.oil               0.793055         0.622260            1.274           0.202
L7.n225             -0.006948         0.006720           -1.034           0.301
L7.jp_unemp         -6.487092        41.692998           -0.156           0.876
L7.jp_gdp           -0.001049         0.000815           -1.287           0.198
L7.usdjpy           -2.516493         2.782723           -0.904           0.366
L8.tokyo            -0.042823         0.037589           -1.139           0.255
L8.oil              -0.417578         0.626188           -0.667           0.505
L8.n225             -0.014279         0.006686           -2.136           0.033
L8.jp_unemp         -4.160973        41.664888           -0.100           0.920
L8.jp_gdp            0.001056         0.000810            1.304           0.192
L8.usdjpy            0.799687         2.789571            0.287           0.774
L9.tokyo            -0.026800         0.037600           -0.713           0.476
L9.oil               0.297287         0.628155            0.473           0.636
L9.n225             -0.020012         0.006737           -2.970           0.003
L9.jp_unemp         -8.968359        41.684022           -0.215           0.830
L9.jp_gdp           -0.000988         0.000800           -1.235           0.217
L9.usdjpy           10.575145         2.817773            3.753           0.000
L10.tokyo            0.008431         0.037531            0.225           0.822
L10.oil              0.264688         0.624534            0.424           0.672
L10.n225            -0.010589         0.006746           -1.570           0.116
L10.jp_unemp       -11.403659        41.717569           -0.273           0.785
L10.jp_gdp          -0.000192         0.000790           -0.244           0.808
L10.usdjpy           1.032596         2.829702            0.365           0.715
L11.tokyo            0.068684         0.037497            1.832           0.067
L11.oil              0.184171         0.623367            0.295           0.768
L11.n225            -0.014514         0.006707           -2.164           0.030
L11.jp_unemp        19.063912        41.712303            0.457           0.648
L11.jp_gdp           0.000152         0.000786            0.194           0.846
L11.usdjpy           2.438795         2.833278            0.861           0.389
L12.tokyo           -0.055958         0.037826           -1.479           0.139
L12.oil             -0.491436         0.618963           -0.794           0.427
L12.n225             0.005143         0.006817            0.754           0.451
L12.jp_unemp        -9.441946        41.696194           -0.226           0.821
L12.jp_gdp           0.000045         0.000772            0.058           0.953
L12.usdjpy           0.612623         2.849921            0.215           0.830
L13.tokyo            0.003381         0.037771            0.090           0.929
L13.oil             -0.615713         0.605055           -1.018           0.309
L13.n225             0.001385         0.006736            0.206           0.837
L13.jp_unemp         7.863036        41.672508            0.189           0.850
L13.jp_gdp          -0.000373         0.000772           -0.483           0.629
L13.usdjpy          -2.481389         2.826686           -0.878           0.380
L14.tokyo            0.037451         0.037890            0.988           0.323
L14.oil              0.106331         0.554207            0.192           0.848
L14.n225            -0.012502         0.006650           -1.880           0.060
L14.jp_unemp        10.946918        41.826029            0.262           0.794
L14.jp_gdp          -0.000966         0.000951           -1.015           0.310
L14.usdjpy          -1.279820         2.767218           -0.462           0.644
===============================================================================

Results for equation oil
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const               -0.072995         0.061202           -1.193           0.233
L1.tokyo            -0.000795         0.001744           -0.456           0.649
L1.oil              -0.244692         0.032305           -7.574           0.000
L1.n225             -0.000053         0.000306           -0.175           0.861
L1.jp_unemp          0.733254         1.972124            0.372           0.710
L1.jp_gdp           -0.000045         0.000040           -1.128           0.259
L1.usdjpy           -0.073698         0.131585           -0.560           0.575
L2.tokyo             0.001653         0.001745            0.947           0.344
L2.oil              -0.160465         0.030071           -5.336           0.000
L2.n225              0.000818         0.000309            2.649           0.008
L2.jp_unemp          1.143342         1.971560            0.580           0.562
L2.jp_gdp           -0.000056         0.000040           -1.421           0.155
L2.usdjpy           -0.121798         0.133405           -0.913           0.361
L3.tokyo            -0.003244         0.001747           -1.856           0.063
L3.oil              -0.102085         0.030047           -3.398           0.001
L3.n225              0.000478         0.000310            1.542           0.123
L3.jp_unemp         -0.546758         1.971849           -0.277           0.782
L3.jp_gdp           -0.000009         0.000040           -0.216           0.829
L3.usdjpy           -0.121726         0.133455           -0.912           0.362
L4.tokyo            -0.000241         0.001768           -0.136           0.892
L4.oil              -0.077465         0.029659           -2.612           0.009
L4.n225              0.000684         0.000311            2.198           0.028
L4.jp_unemp         -0.337083         1.971111           -0.171           0.864
L4.jp_gdp            0.000041         0.000039            1.047           0.295
L4.usdjpy           -0.183250         0.133600           -1.372           0.170
L5.tokyo            -0.002437         0.001772           -1.375           0.169
L5.oil               0.004483         0.029655            0.151           0.880
L5.n225              0.000594         0.000313            1.896           0.058
L5.jp_unemp         -0.976173         1.974115           -0.494           0.621
L5.jp_gdp            0.000026         0.000039            0.676           0.499
L5.usdjpy           -0.025115         0.132922           -0.189           0.850
L6.tokyo            -0.001822         0.001774           -1.027           0.305
L6.oil               0.014813         0.029456            0.503           0.615
L6.n225              0.000722         0.000312            2.309           0.021
L6.jp_unemp         -0.229553         1.974582           -0.116           0.907
L6.jp_gdp            0.000025         0.000039            0.646           0.518
L6.usdjpy           -0.113591         0.132580           -0.857           0.392
L7.tokyo             0.001210         0.001780            0.680           0.497
L7.oil              -0.017045         0.029397           -0.580           0.562
L7.n225              0.000517         0.000317            1.630           0.103
L7.jp_unemp         -0.352881         1.969683           -0.179           0.858
L7.jp_gdp            0.000062         0.000039            1.614           0.107
L7.usdjpy           -0.174360         0.131463           -1.326           0.185
L8.tokyo            -0.001284         0.001776           -0.723           0.470
L8.oil              -0.025626         0.029583           -0.866           0.386
L8.n225              0.000566         0.000316            1.793           0.073
L8.jp_unemp          0.280090         1.968355            0.142           0.887
L8.jp_gdp            0.000005         0.000038            0.119           0.905
L8.usdjpy           -0.008993         0.131786           -0.068           0.946
L9.tokyo             0.001257         0.001776            0.707           0.479
L9.oil              -0.030816         0.029676           -1.038           0.299
L9.n225              0.000028         0.000318            0.089           0.929
L9.jp_unemp          0.536740         1.969259            0.273           0.785
L9.jp_gdp            0.000052         0.000038            1.389           0.165
L9.usdjpy            0.092555         0.133119            0.695           0.487
L10.tokyo            0.001404         0.001773            0.792           0.428
L10.oil             -0.047731         0.029505           -1.618           0.106
L10.n225             0.000113         0.000319            0.355           0.723
L10.jp_unemp         1.943267         1.970843            0.986           0.324
L10.jp_gdp           0.000018         0.000037            0.474           0.635
L10.usdjpy          -0.100987         0.133682           -0.755           0.450
L11.tokyo           -0.005621         0.001771           -3.173           0.002
L11.oil             -0.062407         0.029449           -2.119           0.034
L11.n225             0.001033         0.000317            3.261           0.001
L11.jp_unemp         0.826217         1.970595            0.419           0.675
L11.jp_gdp           0.000012         0.000037            0.336           0.737
L11.usdjpy          -0.279507         0.133851           -2.088           0.037
L12.tokyo            0.000102         0.001787            0.057           0.954
L12.oil             -0.060194         0.029241           -2.059           0.040
L12.n225             0.000402         0.000322            1.248           0.212
L12.jp_unemp        -1.813176         1.969834           -0.920           0.357
L12.jp_gdp           0.000020         0.000036            0.546           0.585
L12.usdjpy           0.043315         0.134637            0.322           0.748
L13.tokyo            0.000101         0.001784            0.057           0.955
L13.oil              0.001514         0.028584            0.053           0.958
L13.n225             0.000574         0.000318            1.803           0.071
L13.jp_unemp        -7.702875         1.968715           -3.913           0.000
L13.jp_gdp           0.000818         0.000036           22.408           0.000
L13.usdjpy          -0.006521         0.133540           -0.049           0.961
L14.tokyo           -0.000151         0.001790           -0.085           0.933
L14.oil             -0.018899         0.026182           -0.722           0.470
L14.n225            -0.000147         0.000314           -0.469           0.639
L14.jp_unemp         2.995692         1.975967            1.516           0.130
L14.jp_gdp          -0.000470         0.000045          -10.454           0.000
L14.usdjpy          -0.021510         0.130730           -0.165           0.869
===============================================================================

Results for equation n225
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const               10.738970         8.002447            1.342           0.180
L1.tokyo             0.061761         0.228078            0.271           0.787
L1.oil              13.849053         4.223994            3.279           0.001
L1.n225             -0.032734         0.039958           -0.819           0.413
L1.jp_unemp        -21.336992       257.864568           -0.083           0.934
L1.jp_gdp            0.004565         0.005178            0.882           0.378
L1.usdjpy           39.529786        17.205423            2.298           0.022
L2.tokyo            -0.340988         0.228191           -1.494           0.135
L2.oil              15.299042         3.931962            3.891           0.000
L2.n225              0.046154         0.040371            1.143           0.253
L2.jp_unemp       -112.209789       257.790892           -0.435           0.663
L2.jp_gdp            0.004196         0.005176            0.811           0.418
L2.usdjpy           17.289427        17.443401            0.991           0.322
L3.tokyo            -0.576113         0.228493           -2.521           0.012
L3.oil               8.939995         3.928769            2.276           0.023
L3.n225              0.030689         0.040557            0.757           0.449
L3.jp_unemp        327.334916       257.828656            1.270           0.204
L3.jp_gdp           -0.009071         0.005170           -1.754           0.079
L3.usdjpy            9.082241        17.449923            0.520           0.603
L4.tokyo            -0.070402         0.231118           -0.305           0.761
L4.oil               8.304019         3.878079            2.141           0.032
L4.n225              0.032117         0.040684            0.789           0.430
L4.jp_unemp         37.779147       257.732136            0.147           0.883
L4.jp_gdp           -0.003906         0.005099           -0.766           0.444
L4.usdjpy           16.009440        17.468852            0.916           0.359
L5.tokyo             0.278928         0.231674            1.204           0.229
L5.oil               1.573213         3.877497            0.406           0.685
L5.n225             -0.035467         0.040960           -0.866           0.387
L5.jp_unemp         32.214267       258.124928            0.125           0.901
L5.jp_gdp           -0.010327         0.005087           -2.030           0.042
L5.usdjpy            8.026272        17.380143            0.462           0.644
L6.tokyo            -0.267908         0.232005           -1.155           0.248
L6.oil               1.922333         3.851479            0.499           0.618
L6.n225             -0.021587         0.040858           -0.528           0.597
L6.jp_unemp       -268.159001       258.186032           -1.039           0.299
L6.jp_gdp            0.002084         0.005076            0.410           0.681
L6.usdjpy           -4.017911        17.335497           -0.232           0.817
L7.tokyo             0.521061         0.232711            2.239           0.025
L7.oil              -5.974025         3.843817           -1.554           0.120
L7.n225             -0.062365         0.041510           -1.502           0.133
L7.jp_unemp       -139.540626       257.545374           -0.542           0.588
L7.jp_gdp           -0.002175         0.005034           -0.432           0.666
L7.usdjpy            0.400842        17.189395            0.023           0.981
L8.tokyo             0.000855         0.232196            0.004           0.997
L8.oil               5.420432         3.868078            1.401           0.161
L8.n225             -0.084229         0.041303           -2.039           0.041
L8.jp_unemp       -108.884864       257.371731           -0.423           0.672
L8.jp_gdp            0.013536         0.005002            2.706           0.007
L8.usdjpy           12.111315        17.231699            0.703           0.482
L9.tokyo             0.245269         0.232263            1.056           0.291
L9.oil               6.271595         3.880231            1.616           0.106
L9.n225             -0.027861         0.041617           -0.669           0.503
L9.jp_unemp       -135.435012       257.489927           -0.526           0.599
L9.jp_gdp           -0.012814         0.004941           -2.593           0.010
L9.usdjpy           33.808555        17.405907            1.942           0.052
L10.tokyo            0.019107         0.231837            0.082           0.934
L10.oil             -2.815652         3.857861           -0.730           0.465
L10.n225             0.023609         0.041668            0.567           0.571
L10.jp_unemp      -162.581773       257.697151           -0.631           0.528
L10.jp_gdp           0.000457         0.004881            0.094           0.925
L10.usdjpy         -20.225220        17.479595           -1.157           0.247
L11.tokyo            0.551521         0.231625            2.381           0.017
L11.oil             -6.464373         3.850652           -1.679           0.093
L11.n225            -0.045521         0.041430           -1.099           0.272
L11.jp_unemp       125.053411       257.664620            0.485           0.627
L11.jp_gdp           0.004126         0.004856            0.850           0.396
L11.usdjpy           0.999769        17.501686            0.057           0.954
L12.tokyo           -0.231117         0.233657           -0.989           0.323
L12.oil             -1.197107         3.823446           -0.313           0.754
L12.n225             0.022887         0.042112            0.543           0.587
L12.jp_unemp      -278.822703       257.565112           -1.083           0.279
L12.jp_gdp          -0.011449         0.004768           -2.401           0.016
L12.usdjpy           9.760300        17.604489            0.554           0.579
L13.tokyo            0.112013         0.233317            0.480           0.631
L13.oil              1.809845         3.737538            0.484           0.628
L13.n225             0.073661         0.041612            1.770           0.077
L13.jp_unemp       134.964531       257.418799            0.524           0.600
L13.jp_gdp           0.000010         0.004771            0.002           0.998
L13.usdjpy          -0.077492        17.460964           -0.004           0.996
L14.tokyo            0.296407         0.234056            1.266           0.205
L14.oil              4.228412         3.423439            1.235           0.217
L14.n225            -0.008343         0.041081           -0.203           0.839
L14.jp_unemp       227.460506       258.367130            0.880           0.379
L14.jp_gdp          -0.005190         0.005877           -0.883           0.377
L14.usdjpy         -41.240057        17.093618           -2.413           0.016
===============================================================================

Results for equation jp_unemp
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const                0.000538         0.001056            0.509           0.610
L1.tokyo             0.000004         0.000030            0.119           0.905
L1.oil               0.000533         0.000557            0.957           0.338
L1.n225             -0.000004         0.000005           -0.773           0.439
L1.jp_unemp          0.000422         0.034013            0.012           0.990
L1.jp_gdp            0.000001         0.000001            1.004           0.315
L1.usdjpy            0.005664         0.002269            2.496           0.013
L2.tokyo             0.000006         0.000030            0.193           0.847
L2.oil               0.000477         0.000519            0.919           0.358
L2.n225             -0.000006         0.000005           -1.158           0.247
L2.jp_unemp         -0.001750         0.034004           -0.051           0.959
L2.jp_gdp            0.000000         0.000001            0.261           0.794
L2.usdjpy           -0.001272         0.002301           -0.553           0.580
L3.tokyo             0.000002         0.000030            0.057           0.954
L3.oil               0.000425         0.000518            0.820           0.412
L3.n225              0.000006         0.000005            1.070           0.285
L3.jp_unemp         -0.001362         0.034009           -0.040           0.968
L3.jp_gdp            0.000000         0.000001            0.379           0.704
L3.usdjpy           -0.000446         0.002302           -0.194           0.846
L4.tokyo             0.000028         0.000030            0.917           0.359
L4.oil               0.000156         0.000512            0.305           0.760
L4.n225             -0.000007         0.000005           -1.235           0.217
L4.jp_unemp         -0.004197         0.033996           -0.123           0.902
L4.jp_gdp            0.000000         0.000001            0.069           0.945
L4.usdjpy            0.001878         0.002304            0.815           0.415
L5.tokyo            -0.000014         0.000031           -0.442           0.658
L5.oil               0.000193         0.000511            0.378           0.705
L5.n225             -0.000001         0.000005           -0.248           0.804
L5.jp_unemp         -0.003547         0.034048           -0.104           0.917
L5.jp_gdp           -0.000000         0.000001           -0.225           0.822
L5.usdjpy           -0.002035         0.002293           -0.888           0.375
L6.tokyo             0.000013         0.000031            0.440           0.660
L6.oil               0.000078         0.000508            0.153           0.878
L6.n225              0.000004         0.000005            0.695           0.487
L6.jp_unemp          0.001988         0.034056            0.058           0.953
L6.jp_gdp            0.000000         0.000001            0.372           0.710
L6.usdjpy           -0.001954         0.002287           -0.855           0.393
L7.tokyo            -0.000035         0.000031           -1.156           0.248
L7.oil               0.000159         0.000507            0.314           0.754
L7.n225              0.000000         0.000005            0.056           0.955
L7.jp_unemp         -0.001502         0.033971           -0.044           0.965
L7.jp_gdp           -0.000000         0.000001           -0.343           0.732
L7.usdjpy            0.001546         0.002267            0.682           0.495
L8.tokyo            -0.000011         0.000031           -0.347           0.729
L8.oil              -0.001120         0.000510           -2.195           0.028
L8.n225             -0.000005         0.000005           -0.855           0.393
L8.jp_unemp         -0.006484         0.033948           -0.191           0.849
L8.jp_gdp           -0.000000         0.000001           -0.336           0.737
L8.usdjpy            0.001447         0.002273            0.637           0.524
L9.tokyo             0.000049         0.000031            1.588           0.112
L9.oil              -0.000562         0.000512           -1.099           0.272
L9.n225             -0.000006         0.000005           -1.013           0.311
L9.jp_unemp          0.006847         0.033964            0.202           0.840
L9.jp_gdp           -0.000000         0.000001           -0.728           0.467
L9.usdjpy            0.002906         0.002296            1.266           0.206
L10.tokyo            0.000019         0.000031            0.628           0.530
L10.oil             -0.000191         0.000509           -0.376           0.707
L10.n225            -0.000005         0.000005           -0.997           0.319
L10.jp_unemp         0.000367         0.033991            0.011           0.991
L10.jp_gdp           0.000000         0.000001            0.104           0.917
L10.usdjpy           0.000764         0.002306            0.331           0.740
L11.tokyo            0.000010         0.000031            0.323           0.746
L11.oil             -0.000232         0.000508           -0.457           0.647
L11.n225             0.000002         0.000005            0.437           0.662
L11.jp_unemp        -0.008212         0.033987           -0.242           0.809
L11.jp_gdp          -0.000000         0.000001           -0.289           0.773
L11.usdjpy           0.002479         0.002309            1.074           0.283
L12.tokyo           -0.000021         0.000031           -0.672           0.502
L12.oil              0.000199         0.000504            0.394           0.694
L12.n225             0.000000         0.000006            0.076           0.939
L12.jp_unemp        -0.005556         0.033974           -0.164           0.870
L12.jp_gdp           0.000000         0.000001            0.104           0.917
L12.usdjpy           0.000321         0.002322            0.138           0.890
L13.tokyo            0.000017         0.000031            0.558           0.577
L13.oil             -0.000090         0.000493           -0.182           0.855
L13.n225            -0.000002         0.000005           -0.369           0.712
L13.jp_unemp        -0.003413         0.033955           -0.101           0.920
L13.jp_gdp          -0.000000         0.000001           -0.017           0.986
L13.usdjpy          -0.000799         0.002303           -0.347           0.729
L14.tokyo           -0.000023         0.000031           -0.748           0.454
L14.oil              0.000018         0.000452            0.040           0.968
L14.n225            -0.000010         0.000005           -1.776           0.076
L14.jp_unemp        -0.012243         0.034080           -0.359           0.719
L14.jp_gdp          -0.000001         0.000001           -0.680           0.496
L14.usdjpy           0.002463         0.002255            1.092           0.275
===============================================================================

Results for equation jp_gdp
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const              -27.057165        52.259649           -0.518           0.605
L1.tokyo             2.962936         1.489451            1.989           0.047
L1.oil             -15.546829        27.584616           -0.564           0.573
L1.n225              0.024418         0.260943            0.094           0.925
L1.jp_unemp         10.654805      1683.973919            0.006           0.995
L1.jp_gdp           -0.038952         0.033812           -1.152           0.249
L1.usdjpy         -169.784876       112.359306           -1.511           0.131
L2.tokyo             0.040784         1.490190            0.027           0.978
L2.oil              12.888738        25.677516            0.502           0.616
L2.n225             -0.194535         0.263639           -0.738           0.461
L2.jp_unemp       -284.247643      1683.492776           -0.169           0.866
L2.jp_gdp           -0.027332         0.033804           -0.809           0.419
L2.usdjpy          269.376209       113.913412            2.365           0.018
L3.tokyo            -5.143803         1.492163           -3.447           0.001
L3.oil              40.216057        25.656662            1.567           0.117
L3.n225             -0.113964         0.264857           -0.430           0.667
L3.jp_unemp       -269.516801      1683.739395           -0.160           0.873
L3.jp_gdp           -0.011941         0.033764           -0.354           0.724
L3.usdjpy          206.319516       113.956003            1.811           0.070
L4.tokyo             1.852296         1.509307            1.227           0.220
L4.oil              29.887224        25.325633            1.180           0.238
L4.n225              0.548712         0.265687            2.065           0.039
L4.jp_unemp        700.400878      1683.109075            0.416           0.677
L4.jp_gdp            0.020001         0.033298            0.601           0.548
L4.usdjpy           -7.989087       114.079619           -0.070           0.944
L5.tokyo            -3.760420         1.512939           -2.486           0.013
L5.oil               4.808553        25.321835            0.190           0.849
L5.n225             -1.012478         0.267488           -3.785           0.000
L5.jp_unemp      -1035.359735      1685.674184           -0.614           0.539
L5.jp_gdp            0.013122         0.033223            0.395           0.693
L5.usdjpy          131.827783       113.500304            1.161           0.245
L6.tokyo             5.129634         1.515097            3.386           0.001
L6.oil              11.095763        25.151925            0.441           0.659
L6.n225             -1.412947         0.266820           -5.296           0.000
L6.jp_unemp       -706.967467      1686.073223           -0.419           0.675
L6.jp_gdp            0.046131         0.033150            1.392           0.164
L6.usdjpy          126.330127       113.208750            1.116           0.264
L7.tokyo             0.521069         1.519709            0.343           0.732
L7.oil              49.068629        25.101891            1.955           0.051
L7.n225             -0.246469         0.271082           -0.909           0.363
L7.jp_unemp        388.504703      1681.889431            0.231           0.817
L7.jp_gdp            0.002133         0.032877            0.065           0.948
L7.usdjpy         -319.093216       112.254631           -2.843           0.004
L8.tokyo            -3.683877         1.516346           -2.429           0.015
L8.oil              25.664734        25.260325            1.016           0.310
L8.n225              0.515541         0.269726            1.911           0.056
L8.jp_unemp        187.806143      1680.755462            0.112           0.911
L8.jp_gdp            0.039789         0.032663            1.218           0.223
L8.usdjpy         -249.634684       112.530898           -2.218           0.027
L9.tokyo            -2.307202         1.516786           -1.521           0.128
L9.oil              42.677158        25.339689            1.684           0.092
L9.n225              0.504498         0.271776            1.856           0.063
L9.jp_unemp       -402.315312      1681.527338           -0.239           0.811
L9.jp_gdp            0.013279         0.032267            0.412           0.681
L9.usdjpy         -274.113842       113.668559           -2.412           0.016
L10.tokyo           -2.470682         1.514005           -1.632           0.103
L10.oil             43.316689        25.193604            1.719           0.086
L10.n225             0.151665         0.272114            0.557           0.577
L10.jp_unemp      1155.594948      1682.880607            0.687           0.492
L10.jp_gdp          -0.015464         0.031875           -0.485           0.628
L10.usdjpy         -10.696199       114.149775           -0.094           0.925
L11.tokyo           -1.556199         1.512620           -1.029           0.304
L11.oil             14.518398        25.146522            0.577           0.564
L11.n225             1.200059         0.270559            4.435           0.000
L11.jp_unemp      1541.942372      1682.668164            0.916           0.359
L11.jp_gdp          -0.013332         0.031715           -0.420           0.674
L11.usdjpy        -487.008962       114.294037           -4.261           0.000
L12.tokyo            1.520000         1.525886            0.996           0.319
L12.oil            -13.679541        24.968858           -0.548           0.584
L12.n225             0.412218         0.275009            1.499           0.134
L12.jp_unemp        -1.400201      1682.018334           -0.001           0.999
L12.jp_gdp          -0.031785         0.031137           -1.021           0.307
L12.usdjpy        -185.869922       114.965387           -1.617           0.106
L13.tokyo            2.292035         1.523669            1.504           0.133
L13.oil            -25.431535        24.407836           -1.042           0.297
L13.n225             0.283730         0.271747            1.044           0.296
L13.jp_unemp      1018.470439      1681.062840            0.606           0.545
L13.jp_gdp           0.002688         0.031157            0.086           0.931
L13.usdjpy         -69.938741       114.028106           -0.613           0.540
L14.tokyo           -1.081139         1.528495           -0.707           0.479
L14.oil              7.790325        22.356626            0.348           0.727
L14.n225             0.191125         0.268278            0.712           0.476
L14.jp_unemp      -414.968883      1687.255880           -0.246           0.806
L14.jp_gdp           0.002682         0.038379            0.070           0.944
L14.usdjpy        -380.841542       111.629170           -3.412           0.001
===============================================================================

Results for equation usdjpy
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const               -0.012941         0.016903           -0.766           0.444
L1.tokyo             0.000344         0.000482            0.715           0.475
L1.oil               0.017695         0.008922            1.983           0.047
L1.n225              0.000281         0.000084            3.335           0.001
L1.jp_unemp         -0.115165         0.544672           -0.211           0.833
L1.jp_gdp            0.000003         0.000011            0.277           0.782
L1.usdjpy           -0.085370         0.036342           -2.349           0.019
L2.tokyo            -0.000238         0.000482           -0.493           0.622
L2.oil               0.000051         0.008305            0.006           0.995
L2.n225             -0.000140         0.000085           -1.645           0.100
L2.jp_unemp          0.125219         0.544516            0.230           0.818
L2.jp_gdp            0.000003         0.000011            0.284           0.776
L2.usdjpy            0.068602         0.036845            1.862           0.063
L3.tokyo             0.000657         0.000483            1.360           0.174
L3.oil               0.002288         0.008298            0.276           0.783
L3.n225             -0.000189         0.000086           -2.205           0.027
L3.jp_unemp          1.020634         0.544596            1.874           0.061
L3.jp_gdp           -0.000008         0.000011           -0.691           0.490
L3.usdjpy            0.028265         0.036858            0.767           0.443
L4.tokyo             0.000414         0.000488            0.848           0.397
L4.oil               0.006152         0.008191            0.751           0.453
L4.n225             -0.000087         0.000086           -1.009           0.313
L4.jp_unemp          1.120773         0.544392            2.059           0.040
L4.jp_gdp           -0.000000         0.000011           -0.046           0.963
L4.usdjpy           -0.010167         0.036898           -0.276           0.783
L5.tokyo             0.000161         0.000489            0.329           0.742
L5.oil              -0.000214         0.008190           -0.026           0.979
L5.n225             -0.000025         0.000087           -0.293           0.769
L5.jp_unemp         -1.090493         0.545222           -2.000           0.045
L5.jp_gdp            0.000019         0.000011            1.724           0.085
L5.usdjpy           -0.087724         0.036711           -2.390           0.017
L6.tokyo            -0.000150         0.000490           -0.306           0.760
L6.oil               0.005532         0.008135            0.680           0.496
L6.n225             -0.000014         0.000086           -0.168           0.867
L6.jp_unemp         -0.361075         0.545351           -0.662           0.508
L6.jp_gdp           -0.000002         0.000011           -0.183           0.855
L6.usdjpy            0.040665         0.036617            1.111           0.267
L7.tokyo             0.000452         0.000492            0.919           0.358
L7.oil               0.013116         0.008119            1.616           0.106
L7.n225              0.000199         0.000088            2.273           0.023
L7.jp_unemp          0.414658         0.543997            0.762           0.446
L7.jp_gdp           -0.000007         0.000011           -0.693           0.488
L7.usdjpy           -0.093690         0.036308           -2.580           0.010
L8.tokyo            -0.000312         0.000490           -0.636           0.525
L8.oil              -0.005389         0.008170           -0.660           0.510
L8.n225              0.000094         0.000087            1.074           0.283
L8.jp_unemp          0.628284         0.543631            1.156           0.248
L8.jp_gdp            0.000000         0.000011            0.034           0.973
L8.usdjpy           -0.119717         0.036397           -3.289           0.001
L9.tokyo             0.000007         0.000491            0.014           0.989
L9.oil               0.003111         0.008196            0.380           0.704
L9.n225              0.000024         0.000088            0.274           0.784
L9.jp_unemp         -0.840016         0.543880           -1.544           0.122
L9.jp_gdp            0.000002         0.000010            0.183           0.855
L9.usdjpy           -0.025266         0.036765           -0.687           0.492
L10.tokyo            0.000047         0.000490            0.095           0.924
L10.oil             -0.002782         0.008149           -0.341           0.733
L10.n225             0.000066         0.000088            0.754           0.451
L10.jp_unemp        -0.193857         0.544318           -0.356           0.722
L10.jp_gdp           0.000009         0.000010            0.826           0.409
L10.usdjpy          -0.085370         0.036921           -2.312           0.021
L11.tokyo            0.000928         0.000489            1.898           0.058
L11.oil             -0.005138         0.008133           -0.632           0.528
L11.n225            -0.000148         0.000088           -1.690           0.091
L11.jp_unemp         0.275886         0.544249            0.507           0.612
L11.jp_gdp          -0.000016         0.000010           -1.588           0.112
L11.usdjpy          -0.008751         0.036968           -0.237           0.813
L12.tokyo           -0.000358         0.000494           -0.724           0.469
L12.oil             -0.003223         0.008076           -0.399           0.690
L12.n225            -0.000079         0.000089           -0.888           0.374
L12.jp_unemp         0.024623         0.544039            0.045           0.964
L12.jp_gdp          -0.000004         0.000010           -0.428           0.669
L12.usdjpy           0.027025         0.037185            0.727           0.467
L13.tokyo            0.000744         0.000493            1.509           0.131
L13.oil              0.003377         0.007895            0.428           0.669
L13.n225            -0.000037         0.000088           -0.418           0.676
L13.jp_unemp         0.243576         0.543730            0.448           0.654
L13.jp_gdp           0.000010         0.000010            1.035           0.300
L13.usdjpy           0.039907         0.036882            1.082           0.279
L14.tokyo           -0.000213         0.000494           -0.432           0.666
L14.oil              0.015281         0.007231            2.113           0.035
L14.n225            -0.000013         0.000087           -0.152           0.879
L14.jp_unemp         0.638267         0.545733            1.170           0.242
L14.jp_gdp          -0.000016         0.000012           -1.322           0.186
L14.usdjpy           0.003866         0.036106            0.107           0.915
===============================================================================

Correlation matrix of residuals
               tokyo       oil      n225  jp_unemp    jp_gdp    usdjpy
tokyo       1.000000  0.064813  0.401044 -0.095193  0.020429  0.108723
oil         0.064813  1.000000  0.164610 -0.004623 -0.006896  0.054685
n225        0.401044  0.164610  1.000000 -0.088557  0.062500  0.372348
jp_unemp   -0.095193 -0.004623 -0.088557  1.000000  0.076504 -0.017203
jp_gdp      0.020429 -0.006896  0.062500  0.076504  1.000000 -0.023702
usdjpy      0.108723  0.054685  0.372348 -0.017203 -0.023702  1.000000


# Calculate yhat
yhat_var2_5 = var2_model5.forecast(var_model5.endog, steps=len(test_diff5))


# clean up yhat
df_yhat_var2_5 = pd.DataFrame(yhat_var2_5)
df_yhat_var2_5.index = test_diff5.index
df_yhat_var2_5.columns = test_diff5.columns
df_yhat_var2_5


# Recover first order differencing
df_pred_var2_5 = pd.concat([tokyo_5[tokyo_5.index==pd.datetime(2020,12,30)], df_yhat_var2_5], axis=0).cumsum()
df_pred_var2_5 = df_pred_var2_5[df_pred_var2_5.index!=pd.datetime(2020,12,30)]

y_pred_var2_5 = df_pred_var2_5["tokyo"]


fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_var2_5.plot(ax=ax, label="VAR(14) with Oil, N225, Unemployement, GDP, USD-JPY", linestyle="dashed")
plt.legend()
plt.show()


var2_metrics5 = calc_metrics(y_test, y_pred_var2_5, return_dict=True)

Test Error Metrics
MAE: 149.9029
MSE: 33680.3447
MAPE: 0.072
sMAPE: 0.0684
MASE: -6.441


# Merge data and fill NAs with interpolation
tokyo_6 = pd.concat([tokyo, gdp_s, unemp_s, oil_s, usdjpy_s, interest_s, n225_s], axis=1)
tokyo_6["jp_gdp"] = tokyo_6["jp_gdp"].fillna(method="ffill")
tokyo_6["jp_unemp"] = tokyo_6["jp_unemp"].fillna(method="ffill")
tokyo_6 = tokyo_6.dropna(subset=["tokyo"])
tokyo_6["oil"] = tokyo_6["oil"].interpolate()
tokyo_6["n225"] = tokyo_6["n225"].interpolate()
tokyo_6["usdjpy"] = tokyo_6["usdjpy"].interpolate()
tokyo_6[tokyo_6.isnull().any(axis=1)]


# Take first difference
tokyo_6_diff = tokyo_6.diff().dropna()


# Split diff into train/test
train_diff6 = tokyo_6_diff[tokyo_6_diff.index.year!=2021]
test_diff6 = tokyo_6_diff[tokyo_6_diff.index.year==2021]


from statsmodels.tsa.vector_ar.var_model import VAR
var_model6=VAR(train_diff)

results_aic6 =[]
for p in range(1,21):
    results6 = var_model6.fit(p)
    results_aic6.append(results6.aic)


# Min=2
plt.plot(list(np.arange(1,21,1)), results_aic, marker="o")
plt.xlabel("Order")
plt.ylabel("AIC")
plt.show()


var2_model6 = var_model6.fit(15)
print(var2_model6.summary())

  Summary of Regression Results   
==================================
Model:                         VAR
Method:                        OLS
Date:           Wed, 01, Jun, 2022
Time:                     18:49:05
--------------------------------------------------------------------
No. of Equations:         7.00000    BIC:                    20.9383
Nobs:                     959.000    HQIC:                   18.6073
Log likelihood:          -17018.0    FPE:                2.89134e+07
AIC:                      17.1735    Det(Omega_mle):     1.38798e+07
--------------------------------------------------------------------
Results for equation tokyo
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const                0.765500         1.287345            0.595           0.552
L1.tokyo             0.018599         0.037006            0.503           0.615
L1.jp_gdp            0.000939         0.000856            1.097           0.273
L1.jp_unemp        -24.482515        41.668023           -0.588           0.557
L1.oil               0.065695         0.722961            0.091           0.928
L1.usdjpy            4.839987         2.938789            1.647           0.100
L1.jp_i            -70.211361       113.014763           -0.621           0.534
L1.n225             -0.004690         0.006671           -0.703           0.482
L2.tokyo            -0.059075         0.036956           -1.599           0.110
L2.jp_gdp           -0.000248         0.000855           -0.290           0.772
L2.jp_unemp         29.081276        41.526120            0.700           0.484
L2.oil              -0.111585         0.714270           -0.156           0.876
L2.usdjpy           -0.175828         2.992989           -0.059           0.953
L2.jp_i            -43.058902       113.262907           -0.380           0.704
L2.n225              0.002570         0.006756            0.380           0.704
L3.tokyo            -0.103305         0.036983           -2.793           0.005
L3.jp_gdp           -0.000446         0.000850           -0.525           0.599
L3.jp_unemp         21.894382        41.528052            0.527           0.598
L3.oil              -0.088623         0.656726           -0.135           0.893
L3.usdjpy            0.260057         2.988348            0.087           0.931
L3.jp_i            -40.087496       114.024124           -0.352           0.725
L3.n225              0.005448         0.006770            0.805           0.421
L4.tokyo            -0.092221         0.037522           -2.458           0.014
L4.jp_gdp            0.000230         0.000844            0.272           0.785
L4.jp_unemp        -19.134873        41.623662           -0.460           0.646
L4.oil               1.182748         0.642743            1.840           0.066
L4.usdjpy            2.805730         2.972899            0.944           0.345
L4.jp_i            -19.501817       114.494178           -0.170           0.865
L4.n225             -0.003245         0.006775           -0.479           0.632
L5.tokyo             0.082068         0.037493            2.189           0.029
L5.jp_gdp           -0.000792         0.000833           -0.951           0.342
L5.jp_unemp         16.807841        41.614882            0.404           0.686
L5.oil               1.620691         0.631048            2.568           0.010
L5.usdjpy           -5.155253         2.989190           -1.725           0.085
L5.jp_i            155.005676       114.754355            1.351           0.177
L5.n225             -0.001848         0.006826           -0.271           0.787
L6.tokyo            -0.082641         0.037714           -2.191           0.028
L6.jp_gdp            0.000385         0.000840            0.459           0.647
L6.jp_unemp        -38.744694        41.717174           -0.929           0.353
L6.oil               0.341885         0.628071            0.544           0.586
L6.usdjpy            1.174448         2.987053            0.393           0.694
L6.jp_i            179.410995       114.847149            1.562           0.118
L6.n225              0.007024         0.006883            1.021           0.307
L7.tokyo             0.015334         0.037775            0.406           0.685
L7.jp_gdp           -0.000906         0.000832           -1.089           0.276
L7.jp_unemp        -11.817876        41.645759           -0.284           0.777
L7.oil               0.807383         0.623749            1.294           0.196
L7.usdjpy           -2.195959         2.960645           -0.742           0.458
L7.jp_i            185.905786       114.984291            1.617           0.106
L7.n225             -0.009272         0.006928           -1.338           0.181
L8.tokyo            -0.040240         0.037696           -1.067           0.286
L8.jp_gdp            0.000885         0.000826            1.070           0.284
L8.jp_unemp         -0.696048        41.510859           -0.017           0.987
L8.oil              -0.339195         0.627801           -0.540           0.589
L8.usdjpy            1.792026         2.969455            0.603           0.546
L8.jp_i           -136.665851       115.724103           -1.181           0.238
L8.n225             -0.014145         0.006958           -2.033           0.042
L9.tokyo            -0.010814         0.037576           -0.288           0.774
L9.jp_gdp           -0.001627         0.000816           -1.994           0.046
L9.jp_unemp         -2.491492        41.485082           -0.060           0.952
L9.oil               0.523349         0.630203            0.830           0.406
L9.usdjpy            9.357711         2.962546            3.159           0.002
L9.jp_i            146.199856       115.445505            1.266           0.205
L9.n225             -0.021935         0.006912           -3.174           0.002
L10.tokyo            0.006590         0.037513            0.176           0.861
L10.jp_gdp          -0.000295         0.000807           -0.366           0.715
L10.jp_unemp        -8.376963        41.634355           -0.201           0.841
L10.oil              0.745498         0.629982            1.183           0.237
L10.usdjpy           1.267971         2.985562            0.425           0.671
L10.jp_i           137.386783       116.430503            1.180           0.238
L10.n225            -0.013811         0.006958           -1.985           0.047
L11.tokyo            0.065588         0.037379            1.755           0.079
L11.jp_gdp           0.000230         0.000790            0.292           0.770
L11.jp_unemp        23.105471        41.622392            0.555           0.579
L11.oil              0.192635         0.624680            0.308           0.758
L11.usdjpy           4.067862         2.967889            1.371           0.170
L11.jp_i          -209.286914       116.429171           -1.798           0.072
L11.n225            -0.009614         0.006950           -1.383           0.167
L12.tokyo           -0.046494         0.037813           -1.230           0.219
L12.jp_gdp           0.000048         0.000787            0.061           0.951
L12.jp_unemp        -8.794786        41.589055           -0.211           0.833
L12.oil             -0.504642         0.623642           -0.809           0.418
L12.usdjpy          -1.471068         2.982102           -0.493           0.622
L12.jp_i            36.541803       116.671376            0.313           0.754
L12.n225             0.005704         0.007011            0.813           0.416
L13.tokyo           -0.002070         0.037681           -0.055           0.956
L13.jp_gdp          -0.000668         0.000775           -0.862           0.389
L13.jp_unemp        -2.373335        41.589082           -0.057           0.954
L13.oil             -0.457385         0.618246           -0.740           0.459
L13.usdjpy          -4.003487         2.948699           -1.358           0.175
L13.jp_i           178.815053       117.169023            1.526           0.127
L13.n225             0.002375         0.007003            0.339           0.735
L14.tokyo            0.032230         0.037720            0.854           0.393
L14.jp_gdp          -0.000950         0.000971           -0.979           0.328
L14.jp_unemp         6.110224        41.943320            0.146           0.884
L14.oil             -0.030356         0.604672           -0.050           0.960
L14.usdjpy           1.045376         2.920790            0.358           0.720
L14.jp_i           165.893685       116.998115            1.418           0.156
L14.n225            -0.015803         0.006954           -2.272           0.023
L15.tokyo            0.103335         0.037868            2.729           0.006
L15.jp_gdp           0.000587         0.001008            0.582           0.560
L15.jp_unemp        -5.840750        42.030339           -0.139           0.889
L15.oil             -0.396975         0.556007           -0.714           0.475
L15.usdjpy           7.286317         2.854421            2.553           0.011
L15.jp_i          -126.233884       116.325443           -1.085           0.278
L15.n225            -0.024442         0.006819           -3.584           0.000
===============================================================================

Results for equation jp_gdp
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const              -17.007450        50.783398           -0.335           0.738
L1.tokyo             2.898491         1.459833            1.985           0.047
L1.jp_gdp           -0.043520         0.033766           -1.289           0.197
L1.jp_unemp         -2.772204      1643.726705           -0.002           0.999
L1.oil             -28.491569        28.519497           -0.999           0.318
L1.usdjpy         -135.592659       115.929810           -1.170           0.242
L1.jp_i          -2163.963979      4458.224076           -0.485           0.627
L1.n225             -0.041151         0.263159           -0.156           0.876
L2.tokyo             0.279921         1.457854            0.192           0.848
L2.jp_gdp           -0.036397         0.033734           -1.079           0.281
L2.jp_unemp       -421.223476      1638.128882           -0.257           0.797
L2.oil              44.172094        28.176654            1.568           0.117
L2.usdjpy          280.371908       118.067903            2.375           0.018
L2.jp_i          -2049.545811      4468.012880           -0.459           0.646
L2.n225             -0.172870         0.266506           -0.649           0.517
L3.tokyo            -4.415699         1.458919           -3.027           0.002
L3.jp_gdp           -0.039572         0.033533           -1.180           0.238
L3.jp_unemp       -143.014812      1638.205091           -0.087           0.930
L3.oil              55.292149        25.906636            2.134           0.033
L3.usdjpy          218.736427       117.884830            1.856           0.064
L3.jp_i          -3004.766925      4498.041500           -0.668           0.504
L3.n225              0.013487         0.267072            0.050           0.960
L4.tokyo             1.295774         1.480186            0.875           0.381
L4.jp_gdp            0.016084         0.033305            0.483           0.629
L4.jp_unemp       -111.184664      1641.976750           -0.068           0.946
L4.oil              39.986709        25.355012            1.577           0.115
L4.usdjpy           15.922992       117.275379            0.136           0.892
L4.jp_i          -1719.765713      4516.584252           -0.381           0.703
L4.n225              0.471891         0.267264            1.766           0.077
L5.tokyo            -3.499918         1.479029           -2.366           0.018
L5.jp_gdp            0.022106         0.032868            0.673           0.501
L5.jp_unemp      -1914.865460      1641.630385           -1.166           0.243
L5.oil              10.189144        24.893661            0.409           0.682
L5.usdjpy           87.549468       117.918048            0.742           0.458
L5.jp_i           6069.022236      4526.847757            1.341           0.180
L5.n225             -0.973228         0.269276           -3.614           0.000
L6.tokyo             5.424702         1.487737            3.646           0.000
L6.jp_gdp            0.043535         0.033126            1.314           0.189
L6.jp_unemp      -1270.640563      1645.665601           -0.772           0.440
L6.oil              19.436848        24.776225            0.784           0.433
L6.usdjpy          176.673591       117.833737            1.499           0.134
L6.jp_i           3706.665373      4530.508326            0.818           0.413
L6.n225             -1.282008         0.271504           -4.722           0.000
L7.tokyo             0.275020         1.490158            0.185           0.854
L7.jp_gdp           -0.003007         0.032810           -0.092           0.927
L7.jp_unemp       -253.978324      1642.848407           -0.155           0.877
L7.oil              46.879887        24.605765            1.905           0.057
L7.usdjpy         -332.993600       116.791969           -2.851           0.004
L7.jp_i           9460.238010      4535.918311            2.086           0.037
L7.n225             -0.411634         0.273287           -1.506           0.132
L8.tokyo            -2.687254         1.487023           -1.807           0.071
L8.jp_gdp            0.056054         0.032599            1.720           0.086
L8.jp_unemp       -129.751054      1637.526864           -0.079           0.937
L8.oil              19.895238        24.765579            0.803           0.422
L8.usdjpy          -86.086628       117.139513           -0.735           0.462
L8.jp_i          -9204.190388      4565.102544           -2.016           0.044
L8.n225              0.331474         0.274483            1.208           0.227
L9.tokyo            -1.676090         1.482291           -1.131           0.258
L9.jp_gdp            0.016558         0.032191            0.514           0.607
L9.jp_unemp       -451.092892      1636.510024           -0.276           0.783
L9.oil              39.272362        24.860329            1.580           0.114
L9.usdjpy         -106.198695       116.866964           -0.909           0.364
L9.jp_i         -11641.364784      4554.112356           -2.556           0.011
L9.n225              0.450838         0.272658            1.653           0.098
L10.tokyo           -2.299631         1.479823           -1.554           0.120
L10.jp_gdp           0.005854         0.031818            0.184           0.854
L10.jp_unemp       678.050044      1642.398564            0.413           0.680
L10.oil             34.361509        24.851625            1.383           0.167
L10.usdjpy          -3.945763       117.774898           -0.034           0.973
L10.jp_i         -6979.735617      4592.968713           -1.520           0.129
L10.n225             0.020164         0.274462            0.073           0.941
L11.tokyo           -1.687552         1.474527           -1.144           0.252
L11.jp_gdp          -0.004969         0.031159           -0.159           0.873
L11.jp_unemp      1606.196714      1641.926656            0.978           0.328
L11.oil              9.354562        24.642470            0.380           0.704
L11.usdjpy        -307.727526       117.077769           -2.628           0.009
L11.jp_i         -3742.856839      4592.916162           -0.815           0.415
L11.n225             1.006287         0.274174            3.670           0.000
L12.tokyo            1.011879         1.491654            0.678           0.498
L12.jp_gdp          -0.025858         0.031065           -0.832           0.405
L12.jp_unemp       162.434594      1640.611570            0.099           0.921
L12.oil            -20.629511        24.601511           -0.839           0.402
L12.usdjpy        -127.053358       117.638437           -1.080           0.280
L12.jp_i        -16061.973197      4602.470717           -3.490           0.000
L12.n225             0.603207         0.276590            2.181           0.029
L13.tokyo            2.159932         1.486462            1.453           0.146
L13.jp_gdp          -0.002076         0.030575           -0.068           0.946
L13.jp_unemp       703.950795      1640.612604            0.429           0.668
L13.oil            -36.256252        24.388675           -1.487           0.137
L13.usdjpy          -0.220838       116.320752           -0.002           0.998
L13.jp_i        -12865.836695      4622.101960           -2.784           0.005
L13.n225             0.397846         0.276252            1.440           0.150
L14.tokyo           -1.129426         1.487989           -0.759           0.448
L14.jp_gdp           0.008589         0.038287            0.224           0.822
L14.jp_unemp      -594.767147      1654.586668           -0.359           0.719
L14.oil              6.914532        23.853205            0.290           0.772
L14.usdjpy        -339.374926       115.219764           -2.945           0.003
L14.jp_i          4571.987608      4615.359969            0.991           0.322
L14.n225            -0.026862         0.274340           -0.098           0.922
L15.tokyo            0.647118         1.493820            0.433           0.665
L15.jp_gdp          -0.063748         0.039780           -1.602           0.109
L15.jp_unemp      1227.556865      1658.019393            0.740           0.459
L15.oil             -5.058086        21.933441           -0.231           0.818
L15.usdjpy          87.754537       112.601649            0.779           0.436
L15.jp_i        -27466.609838      4588.824291           -5.986           0.000
L15.n225             0.282961         0.269004            1.052           0.293
===============================================================================

Results for equation jp_unemp
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const                0.000400         0.001066            0.375           0.708
L1.tokyo             0.000005         0.000031            0.173           0.863
L1.jp_gdp            0.000001         0.000001            0.786           0.432
L1.jp_unemp         -0.001695         0.034515           -0.049           0.961
L1.oil               0.000703         0.000599            1.173           0.241
L1.usdjpy            0.005996         0.002434            2.463           0.014
L1.jp_i              0.075996         0.093614            0.812           0.417
L1.n225             -0.000005         0.000006           -0.995           0.320
L2.tokyo             0.000006         0.000031            0.187           0.852
L2.jp_gdp            0.000000         0.000001            0.306           0.760
L2.jp_unemp         -0.004652         0.034397           -0.135           0.892
L2.oil               0.000272         0.000592            0.460           0.645
L2.usdjpy           -0.000070         0.002479           -0.028           0.978
L2.jp_i             -0.003421         0.093819           -0.036           0.971
L2.n225             -0.000007         0.000006           -1.180           0.238
L3.tokyo             0.000004         0.000031            0.129           0.898
L3.jp_gdp            0.000000         0.000001            0.295           0.768
L3.jp_unemp          0.000224         0.034399            0.007           0.995
L3.oil               0.000215         0.000544            0.395           0.693
L3.usdjpy            0.001047         0.002475            0.423           0.672
L3.jp_i             -0.128947         0.094450           -1.365           0.172
L3.n225              0.000007         0.000006            1.170           0.242
L4.tokyo             0.000040         0.000031            1.278           0.201
L4.jp_gdp           -0.000000         0.000001           -0.123           0.902
L4.jp_unemp         -0.004987         0.034478           -0.145           0.885
L4.oil              -0.000186         0.000532           -0.349           0.727
L4.usdjpy            0.002990         0.002463            1.214           0.225
L4.jp_i             -0.091702         0.094839           -0.967           0.334
L4.n225             -0.000008         0.000006           -1.409           0.159
L5.tokyo            -0.000010         0.000031           -0.311           0.756
L5.jp_gdp           -0.000000         0.000001           -0.027           0.979
L5.jp_unemp         -0.004126         0.034471           -0.120           0.905
L5.oil               0.000048         0.000523            0.093           0.926
L5.usdjpy           -0.001279         0.002476           -0.517           0.605
L5.jp_i             -0.089151         0.095055           -0.938           0.348
L5.n225             -0.000002         0.000006           -0.425           0.671
L6.tokyo             0.000017         0.000031            0.559           0.576
L6.jp_gdp            0.000000         0.000001            0.544           0.587
L6.jp_unemp          0.004797         0.034556            0.139           0.890
L6.oil              -0.000048         0.000520           -0.093           0.926
L6.usdjpy           -0.001728         0.002474           -0.699           0.485
L6.jp_i             -0.049869         0.095131           -0.524           0.600
L6.n225              0.000005         0.000006            0.872           0.383
L7.tokyo            -0.000041         0.000031           -1.300           0.193
L7.jp_gdp           -0.000000         0.000001           -0.510           0.610
L7.jp_unemp         -0.002614         0.034496           -0.076           0.940
L7.oil               0.000065         0.000517            0.126           0.900
L7.usdjpy            0.001699         0.002452            0.693           0.488
L7.jp_i             -0.065119         0.095245           -0.684           0.494
L7.n225              0.000001         0.000006            0.238           0.812
L8.tokyo            -0.000011         0.000031           -0.357           0.721
L8.jp_gdp           -0.000000         0.000001           -0.511           0.610
L8.jp_unemp         -0.007219         0.034385           -0.210           0.834
L8.oil              -0.001284         0.000520           -2.469           0.014
L8.usdjpy            0.001389         0.002460            0.565           0.572
L8.jp_i             -0.081417         0.095858           -0.849           0.396
L8.n225             -0.000003         0.000006           -0.550           0.583
L9.tokyo             0.000047         0.000031            1.505           0.132
L9.jp_gdp           -0.000000         0.000001           -0.442           0.658
L9.jp_unemp          0.004147         0.034363            0.121           0.904
L9.oil              -0.000635         0.000522           -1.217           0.224
L9.usdjpy            0.003732         0.002454            1.521           0.128
L9.jp_i             -0.082910         0.095627           -0.867           0.386
L9.n225             -0.000005         0.000006           -0.906           0.365
L10.tokyo            0.000019         0.000031            0.613           0.540
L10.jp_gdp           0.000000         0.000001            0.220           0.826
L10.jp_unemp        -0.000994         0.034487           -0.029           0.977
L10.oil             -0.000270         0.000522           -0.518           0.604
L10.usdjpy           0.000641         0.002473            0.259           0.795
L10.jp_i            -0.030627         0.096443           -0.318           0.751
L10.n225            -0.000006         0.000006           -1.041           0.298
L11.tokyo            0.000009         0.000031            0.306           0.759
L11.jp_gdp          -0.000000         0.000001           -0.159           0.874
L11.jp_unemp        -0.001897         0.034477           -0.055           0.956
L11.oil             -0.000273         0.000517           -0.527           0.598
L11.usdjpy           0.003200         0.002458            1.302           0.193
L11.jp_i            -0.113660         0.096442           -1.179           0.239
L11.n225             0.000004         0.000006            0.618           0.537
L12.tokyo           -0.000023         0.000031           -0.721           0.471
L12.jp_gdp           0.000000         0.000001            0.254           0.799
L12.jp_unemp        -0.002596         0.034449           -0.075           0.940
L12.oil              0.000033         0.000517            0.063           0.949
L12.usdjpy           0.000337         0.002470            0.136           0.891
L12.jp_i            -0.040731         0.096642           -0.421           0.673
L12.n225             0.000001         0.000006            0.200           0.841
L13.tokyo            0.000013         0.000031            0.425           0.671
L13.jp_gdp           0.000000         0.000001            0.039           0.968
L13.jp_unemp        -0.003525         0.034449           -0.102           0.919
L13.oil             -0.000235         0.000512           -0.458           0.647
L13.usdjpy          -0.001187         0.002442           -0.486           0.627
L13.jp_i            -0.047678         0.097055           -0.491           0.623
L13.n225            -0.000000         0.000006           -0.058           0.954
L14.tokyo           -0.000023         0.000031           -0.739           0.460
L14.jp_gdp          -0.000001         0.000001           -0.920           0.357
L14.jp_unemp        -0.007685         0.034743           -0.221           0.825
L14.oil             -0.000090         0.000501           -0.180           0.857
L14.usdjpy           0.001076         0.002419            0.445           0.657
L14.jp_i             0.086062         0.096913            0.888           0.375
L14.n225            -0.000009         0.000006           -1.501           0.133
L15.tokyo           -0.000027         0.000031           -0.873           0.382
L15.jp_gdp           0.000001         0.000001            0.704           0.481
L15.jp_unemp        -0.003340         0.034815           -0.096           0.924
L15.oil             -0.000197         0.000461           -0.427           0.669
L15.usdjpy          -0.003916         0.002364           -1.656           0.098
L15.jp_i             0.033500         0.096356            0.348           0.728
L15.n225             0.000008         0.000006            1.490           0.136
===============================================================================

Results for equation oil
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const               -0.062749         0.061285           -1.024           0.306
L1.tokyo            -0.001164         0.001762           -0.661           0.509
L1.jp_gdp           -0.000043         0.000041           -1.059           0.290
L1.jp_unemp          0.322426         1.983645            0.163           0.871
L1.oil              -0.289795         0.034417           -8.420           0.000
L1.usdjpy           -0.102528         0.139904           -0.733           0.464
L1.jp_i              1.369191         5.380174            0.254           0.799
L1.n225             -0.000023         0.000318           -0.071           0.943
L2.tokyo             0.001740         0.001759            0.989           0.323
L2.jp_gdp           -0.000049         0.000041           -1.193           0.233
L2.jp_unemp          1.130870         1.976890            0.572           0.567
L2.oil              -0.098452         0.034004           -2.895           0.004
L2.usdjpy           -0.127650         0.142484           -0.896           0.370
L2.jp_i             -0.943841         5.391987           -0.175           0.861
L2.n225              0.000680         0.000322            2.113           0.035
L3.tokyo            -0.002867         0.001761           -1.628           0.103
L3.jp_gdp           -0.000004         0.000040           -0.106           0.915
L3.jp_unemp         -0.322470         1.976982           -0.163           0.870
L3.oil              -0.067987         0.031264           -2.175           0.030
L3.usdjpy           -0.045487         0.142263           -0.320           0.749
L3.jp_i             -2.910279         5.428226           -0.536           0.592
L3.n225              0.000346         0.000322            1.073           0.283
L4.tokyo            -0.000727         0.001786           -0.407           0.684
L4.jp_gdp            0.000048         0.000040            1.185           0.236
L4.jp_unemp         -0.397350         1.981534           -0.201           0.841
L4.oil              -0.055541         0.030598           -1.815           0.069
L4.usdjpy           -0.190623         0.141528           -1.347           0.178
L4.jp_i             -3.945133         5.450603           -0.724           0.469
L4.n225              0.000656         0.000323            2.034           0.042
L5.tokyo            -0.002472         0.001785           -1.385           0.166
L5.jp_gdp            0.000018         0.000040            0.455           0.649
L5.jp_unemp         -0.849547         1.981116           -0.429           0.668
L5.oil               0.018666         0.030042            0.621           0.534
L5.usdjpy            0.014896         0.142303            0.105           0.917
L5.jp_i             -5.002603         5.462989           -0.916           0.360
L5.n225              0.000675         0.000325            2.077           0.038
L6.tokyo            -0.002473         0.001795           -1.378           0.168
L6.jp_gdp            0.000017         0.000040            0.423           0.672
L6.jp_unemp         -0.495242         1.985985           -0.249           0.803
L6.oil               0.030863         0.029900            1.032           0.302
L6.usdjpy           -0.110966         0.142201           -0.780           0.435
L6.jp_i              3.541255         5.467406            0.648           0.517
L6.n225              0.000595         0.000328            1.816           0.069
L7.tokyo             0.001192         0.001798            0.663           0.507
L7.jp_gdp            0.000060         0.000040            1.505           0.132
L7.jp_unemp         -0.367868         1.982585           -0.186           0.853
L7.oil              -0.006219         0.029694           -0.209           0.834
L7.usdjpy           -0.186024         0.140944           -1.320           0.187
L7.jp_i              0.623799         5.473935            0.114           0.909
L7.n225              0.000558         0.000330            1.693           0.090
L8.tokyo            -0.001108         0.001795           -0.617           0.537
L8.jp_gdp            0.000012         0.000039            0.311           0.756
L8.jp_unemp          0.303645         1.976163            0.154           0.878
L8.oil              -0.014149         0.029887           -0.473           0.636
L8.usdjpy            0.013955         0.141364            0.099           0.921
L8.jp_i              5.145874         5.509155            0.934           0.350
L8.n225              0.000431         0.000331            1.301           0.193
L9.tokyo             0.001101         0.001789            0.615           0.538
L9.jp_gdp            0.000047         0.000039            1.217           0.224
L9.jp_unemp          0.695979         1.974936            0.352           0.725
L9.oil              -0.025404         0.030001           -0.847           0.397
L9.usdjpy            0.120365         0.141035            0.853           0.393
L9.jp_i             -8.103896         5.495892           -1.475           0.140
L9.n225              0.000126         0.000329            0.384           0.701
L10.tokyo            0.002059         0.001786            1.153           0.249
L10.jp_gdp           0.000023         0.000038            0.603           0.546
L10.jp_unemp         1.661874         1.982043            0.838           0.402
L10.oil             -0.047962         0.029991           -1.599           0.110
L10.usdjpy          -0.071662         0.142130           -0.504           0.614
L10.jp_i             1.447813         5.542784            0.261           0.794
L10.n225            -0.000085         0.000331           -0.258           0.796
L11.tokyo           -0.005482         0.001779           -3.081           0.002
L11.jp_gdp           0.000012         0.000038            0.322           0.747
L11.jp_unemp         0.583721         1.981473            0.295           0.768
L11.oil             -0.053273         0.029738           -1.791           0.073
L11.usdjpy          -0.326701         0.141289           -2.312           0.021
L11.jp_i             8.561546         5.542720            1.545           0.122
L11.n225             0.000812         0.000331            2.454           0.014
L12.tokyo           -0.000442         0.001800           -0.245           0.806
L12.jp_gdp           0.000005         0.000037            0.142           0.887
L12.jp_unemp        -1.834297         1.979886           -0.926           0.354
L12.oil             -0.052393         0.029689           -1.765           0.078
L12.usdjpy           0.010813         0.141966            0.076           0.939
L12.jp_i             2.997794         5.554251            0.540           0.589
L12.n225             0.000431         0.000334            1.291           0.197
L13.tokyo            0.000388         0.001794            0.216           0.829
L13.jp_gdp           0.000808         0.000037           21.889           0.000
L13.jp_unemp        -7.751676         1.979887           -3.915           0.000
L13.oil              0.000853         0.029432            0.029           0.977
L13.usdjpy           0.010155         0.140376            0.072           0.942
L13.jp_i             2.574621         5.577941            0.462           0.644
L13.n225             0.000523         0.000333            1.568           0.117
L14.tokyo            0.000003         0.001796            0.002           0.999
L14.jp_gdp          -0.000438         0.000046           -9.478           0.000
L14.jp_unemp         2.542084         1.996751            1.273           0.203
L14.oil             -0.018400         0.028786           -0.639           0.523
L14.usdjpy           0.033597         0.139047            0.242           0.809
L14.jp_i            -2.732869         5.569805           -0.491           0.624
L14.n225            -0.000226         0.000331           -0.683           0.495
L15.tokyo           -0.001191         0.001803           -0.661           0.509
L15.jp_gdp          -0.000189         0.000048           -3.946           0.000
L15.jp_unemp         1.252582         2.000894            0.626           0.531
L15.oil              0.004048         0.026469            0.153           0.878
L15.usdjpy           0.204737         0.135887            1.507           0.132
L15.jp_i            -5.427839         5.537782           -0.980           0.327
L15.n225            -0.000087         0.000325           -0.269           0.788
===============================================================================

Results for equation usdjpy
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const               -0.014737         0.016747           -0.880           0.379
L1.tokyo             0.000294         0.000481            0.611           0.541
L1.jp_gdp            0.000001         0.000011            0.081           0.935
L1.jp_unemp         -0.089336         0.542054           -0.165           0.869
L1.oil               0.020585         0.009405            2.189           0.029
L1.usdjpy           -0.096201         0.038230           -2.516           0.012
L1.jp_i              3.256948         1.470194            2.215           0.027
L1.n225              0.000245         0.000087            2.822           0.005
L2.tokyo            -0.000480         0.000481           -0.998           0.318
L2.jp_gdp            0.000001         0.000011            0.070           0.944
L2.jp_unemp          0.124693         0.540208            0.231           0.817
L2.oil               0.000484         0.009292            0.052           0.958
L2.usdjpy            0.042147         0.038935            1.082           0.279
L2.jp_i              2.982425         1.473422            2.024           0.043
L2.n225             -0.000109         0.000088           -1.239           0.215
L3.tokyo             0.000578         0.000481            1.202           0.229
L3.jp_gdp           -0.000011         0.000011           -1.029           0.304
L3.jp_unemp          1.136938         0.540233            2.105           0.035
L3.oil               0.002243         0.008543            0.263           0.793
L3.usdjpy            0.024188         0.038875            0.622           0.534
L3.jp_i             -1.797688         1.483325           -1.212           0.226
L3.n225             -0.000095         0.000088           -1.076           0.282
L4.tokyo             0.000509         0.000488            1.044           0.297
L4.jp_gdp           -0.000005         0.000011           -0.478           0.633
L4.jp_unemp          1.115966         0.541477            2.061           0.039
L4.oil               0.002759         0.008361            0.330           0.741
L4.usdjpy           -0.036157         0.038674           -0.935           0.350
L4.jp_i              4.218768         1.489440            2.832           0.005
L4.n225             -0.000145         0.000088           -1.643           0.100
L5.tokyo             0.000108         0.000488            0.221           0.825
L5.jp_gdp            0.000015         0.000011            1.378           0.168
L5.jp_unemp         -1.014484         0.541362           -1.874           0.061
L5.oil               0.001794         0.008209            0.219           0.827
L5.usdjpy           -0.093479         0.038886           -2.404           0.016
L5.jp_i             -1.154073         1.492824           -0.773           0.439
L5.n225              0.000018         0.000089            0.198           0.843
L6.tokyo            -0.000043         0.000491           -0.087           0.930
L6.jp_gdp            0.000004         0.000011            0.355           0.723
L6.jp_unemp         -0.209097         0.542693           -0.385           0.700
L6.oil               0.004831         0.008170            0.591           0.554
L6.usdjpy            0.021537         0.038858            0.554           0.579
L6.jp_i              3.939511         1.494031            2.637           0.008
L6.n225             -0.000037         0.000090           -0.409           0.683
L7.tokyo             0.000339         0.000491            0.690           0.490
L7.jp_gdp           -0.000010         0.000011           -0.928           0.353
L7.jp_unemp          0.333681         0.541764            0.616           0.538
L7.oil               0.014012         0.008114            1.727           0.084
L7.usdjpy           -0.102818         0.038515           -2.670           0.008
L7.jp_i              0.785871         1.495815            0.525           0.599
L7.n225              0.000190         0.000090            2.114           0.035
L8.tokyo            -0.000325         0.000490           -0.662           0.508
L8.jp_gdp           -0.000002         0.000011           -0.230           0.818
L8.jp_unemp          0.575247         0.540009            1.065           0.287
L8.oil              -0.007469         0.008167           -0.915           0.360
L8.usdjpy           -0.130041         0.038629           -3.366           0.001
L8.jp_i              0.380251         1.505439            0.253           0.801
L8.n225              0.000140         0.000091            1.547           0.122
L9.tokyo             0.000076         0.000489            0.155           0.877
L9.jp_gdp            0.000003         0.000011            0.326           0.745
L9.jp_unemp         -0.922628         0.539674           -1.710           0.087
L9.oil               0.003116         0.008198            0.380           0.704
L9.usdjpy           -0.040929         0.038539           -1.062           0.288
L9.jp_i              3.829285         1.501815            2.550           0.011
L9.n225             -0.000014         0.000090           -0.153           0.879
L10.tokyo           -0.000034         0.000488           -0.069           0.945
L10.jp_gdp           0.000004         0.000010            0.398           0.691
L10.jp_unemp        -0.326307         0.541616           -0.602           0.547
L10.oil             -0.001013         0.008195           -0.124           0.902
L10.usdjpy          -0.092409         0.038839           -2.379           0.017
L10.jp_i             1.878461         1.514629            1.240           0.215
L10.n225             0.000039         0.000091            0.426           0.670
L11.tokyo            0.000969         0.000486            1.993           0.046
L11.jp_gdp          -0.000014         0.000010           -1.371           0.170
L11.jp_unemp         0.403228         0.541460            0.745           0.456
L11.oil             -0.004754         0.008126           -0.585           0.559
L11.usdjpy           0.014005         0.038609            0.363           0.717
L11.jp_i            -1.061309         1.514612           -0.701           0.483
L11.n225            -0.000113         0.000090           -1.255           0.210
L12.tokyo           -0.000403         0.000492           -0.819           0.413
L12.jp_gdp          -0.000004         0.000010           -0.372           0.710
L12.jp_unemp         0.104936         0.541026            0.194           0.846
L12.oil             -0.005276         0.008113           -0.650           0.515
L12.usdjpy           0.033367         0.038794            0.860           0.390
L12.jp_i            -1.060195         1.517762           -0.699           0.485
L12.n225            -0.000101         0.000091           -1.109           0.267
L13.tokyo            0.000717         0.000490            1.463           0.143
L13.jp_gdp           0.000010         0.000010            0.975           0.329
L13.jp_unemp         0.177135         0.541027            0.327           0.743
L13.oil              0.003628         0.008043            0.451           0.652
L13.usdjpy           0.056547         0.038359            1.474           0.140
L13.jp_i            -2.621324         1.524236           -1.720           0.085
L13.n225            -0.000009         0.000091           -0.101           0.920
L14.tokyo           -0.000109         0.000491           -0.222           0.825
L14.jp_gdp          -0.000013         0.000013           -1.006           0.314
L14.jp_unemp         0.726663         0.545635            1.332           0.183
L14.oil              0.013209         0.007866            1.679           0.093
L14.usdjpy          -0.004416         0.037996           -0.116           0.907
L14.jp_i             1.246133         1.522013            0.819           0.413
L14.n225            -0.000032         0.000090           -0.354           0.724
L15.tokyo           -0.000704         0.000493           -1.428           0.153
L15.jp_gdp           0.000009         0.000013            0.721           0.471
L15.jp_unemp        -0.351486         0.546767           -0.643           0.520
L15.oil             -0.000080         0.007233           -0.011           0.991
L15.usdjpy          -0.054338         0.037133           -1.463           0.143
L15.jp_i             0.140151         1.513262            0.093           0.926
L15.n225             0.000004         0.000089            0.042           0.967
===============================================================================

Results for equation jp_i
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const               -0.000117         0.000417           -0.281           0.779
L1.tokyo             0.000020         0.000012            1.656           0.098
L1.jp_gdp            0.000001         0.000000            2.041           0.041
L1.jp_unemp         -0.005470         0.013484           -0.406           0.685
L1.oil              -0.000354         0.000234           -1.515           0.130
L1.usdjpy           -0.000624         0.000951           -0.656           0.512
L1.jp_i             -0.054469         0.036573           -1.489           0.136
L1.n225             -0.000005         0.000002           -2.490           0.013
L2.tokyo            -0.000012         0.000012           -0.975           0.330
L2.jp_gdp            0.000000         0.000000            0.652           0.515
L2.jp_unemp         -0.008007         0.013438           -0.596           0.551
L2.oil               0.000248         0.000231            1.075           0.282
L2.usdjpy            0.000757         0.000969            0.782           0.434
L2.jp_i             -0.079413         0.036653           -2.167           0.030
L2.n225             -0.000002         0.000002           -0.822           0.411
L3.tokyo            -0.000022         0.000012           -1.805           0.071
L3.jp_gdp            0.000000         0.000000            1.427           0.154
L3.jp_unemp          0.013189         0.013439            0.981           0.326
L3.oil               0.000023         0.000213            0.109           0.913
L3.usdjpy            0.000119         0.000967            0.123           0.902
L3.jp_i              0.060693         0.036899            1.645           0.100
L3.n225              0.000003         0.000002            1.529           0.126
L4.tokyo            -0.000003         0.000012           -0.265           0.791
L4.jp_gdp           -0.000000         0.000000           -0.132           0.895
L4.jp_unemp         -0.005366         0.013470           -0.398           0.690
L4.oil              -0.000019         0.000208           -0.091           0.927
L4.usdjpy           -0.002184         0.000962           -2.271           0.023
L4.jp_i              0.000743         0.037052            0.020           0.984
L4.n225              0.000002         0.000002            0.939           0.348
L5.tokyo             0.000006         0.000012            0.493           0.622
L5.jp_gdp           -0.000001         0.000000           -2.818           0.005
L5.jp_unemp         -0.010724         0.013467           -0.796           0.426
L5.oil               0.000136         0.000204            0.668           0.504
L5.usdjpy           -0.001639         0.000967           -1.694           0.090
L5.jp_i              0.010984         0.037136            0.296           0.767
L5.n225              0.000001         0.000002            0.671           0.502
L6.tokyo            -0.000001         0.000012           -0.063           0.950
L6.jp_gdp           -0.000000         0.000000           -0.453           0.650
L6.jp_unemp          0.006545         0.013500            0.485           0.628
L6.oil               0.000369         0.000203            1.816           0.069
L6.usdjpy           -0.000059         0.000967           -0.061           0.951
L6.jp_i             -0.038553         0.037166           -1.037           0.300
L6.n225              0.000003         0.000002            1.516           0.130
L7.tokyo             0.000003         0.000012            0.213           0.831
L7.jp_gdp            0.000000         0.000000            0.648           0.517
L7.jp_unemp         -0.004673         0.013477           -0.347           0.729
L7.oil              -0.000018         0.000202           -0.089           0.929
L7.usdjpy           -0.000492         0.000958           -0.513           0.608
L7.jp_i             -0.036287         0.037210           -0.975           0.329
L7.n225             -0.000003         0.000002           -1.283           0.200
L8.tokyo             0.000007         0.000012            0.572           0.567
L8.jp_gdp            0.000000         0.000000            0.285           0.776
L8.jp_unemp          0.008609         0.013433            0.641           0.522
L8.oil              -0.000059         0.000203           -0.292           0.770
L8.usdjpy           -0.001087         0.000961           -1.131           0.258
L8.jp_i             -0.040442         0.037450           -1.080           0.280
L8.n225             -0.000001         0.000002           -0.271           0.786
L9.tokyo            -0.000002         0.000012           -0.148           0.883
L9.jp_gdp           -0.000000         0.000000           -1.145           0.252
L9.jp_unemp          0.019295         0.013425            1.437           0.151
L9.oil              -0.000170         0.000204           -0.833           0.405
L9.usdjpy           -0.002260         0.000959           -2.357           0.018
L9.jp_i              0.036886         0.037359            0.987           0.323
L9.n225              0.000004         0.000002            1.607           0.108
L10.tokyo           -0.000011         0.000012           -0.927           0.354
L10.jp_gdp          -0.000000         0.000000           -0.984           0.325
L10.jp_unemp        -0.007735         0.013473           -0.574           0.566
L10.oil             -0.000126         0.000204           -0.617           0.537
L10.usdjpy           0.000420         0.000966            0.435           0.664
L10.jp_i             0.067118         0.037678            1.781           0.075
L10.n225             0.000000         0.000002            0.106           0.916
L11.tokyo            0.000023         0.000012            1.867           0.062
L11.jp_gdp           0.000000         0.000000            0.028           0.978
L11.jp_unemp         0.000989         0.013469            0.073           0.941
L11.oil             -0.000345         0.000202           -1.707           0.088
L11.usdjpy           0.001551         0.000960            1.615           0.106
L11.jp_i             0.000315         0.037678            0.008           0.993
L11.n225            -0.000005         0.000002           -2.431           0.015
L12.tokyo           -0.000014         0.000012           -1.166           0.244
L12.jp_gdp          -0.000000         0.000000           -1.169           0.242
L12.jp_unemp        -0.000464         0.013459           -0.034           0.972
L12.oil              0.000127         0.000202            0.628           0.530
L12.usdjpy          -0.000072         0.000965           -0.074           0.941
L12.jp_i             0.016560         0.037756            0.439           0.661
L12.n225            -0.000002         0.000002           -0.685           0.493
L13.tokyo           -0.000005         0.000012           -0.395           0.693
L13.jp_gdp           0.000000         0.000000            0.447           0.655
L13.jp_unemp         0.017783         0.013459            1.321           0.186
L13.oil              0.000072         0.000200            0.362           0.717
L13.usdjpy           0.000384         0.000954            0.402           0.687
L13.jp_i             0.004112         0.037917            0.108           0.914
L13.n225             0.000002         0.000002            0.777           0.437
L14.tokyo           -0.000026         0.000012           -2.162           0.031
L14.jp_gdp           0.000000         0.000000            0.222           0.824
L14.jp_unemp        -0.036981         0.013573           -2.725           0.006
L14.oil              0.000184         0.000196            0.938           0.348
L14.usdjpy           0.000155         0.000945            0.164           0.869
L14.jp_i            -0.066282         0.037862           -1.751           0.080
L14.n225             0.000001         0.000002            0.416           0.678
L15.tokyo           -0.000008         0.000012           -0.663           0.507
L15.jp_gdp           0.000000         0.000000            0.297           0.766
L15.jp_unemp         0.002411         0.013601            0.177           0.859
L15.oil             -0.000123         0.000180           -0.682           0.495
L15.usdjpy           0.000642         0.000924            0.695           0.487
L15.jp_i            -0.007004         0.037644           -0.186           0.852
L15.n225             0.000000         0.000002            0.073           0.942
===============================================================================

Results for equation n225
===============================================================================
                  coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------
const               10.783937         7.958958            1.355           0.175
L1.tokyo             0.108327         0.228790            0.473           0.636
L1.jp_gdp            0.008134         0.005292            1.537           0.124
L1.jp_unemp         59.384256       257.610801            0.231           0.818
L1.oil              13.685156         4.469679            3.062           0.002
L1.usdjpy           52.640040        18.168940            2.897           0.004
L1.jp_i          -2160.429516       698.709019           -3.092           0.002
L1.n225             -0.023978         0.041243           -0.581           0.561
L2.tokyo            -0.303374         0.228480           -1.328           0.184
L2.jp_gdp            0.005109         0.005287            0.966           0.334
L2.jp_unemp        -69.094721       256.733489           -0.269           0.788
L2.oil              14.488216         4.415947            3.281           0.001
L2.usdjpy           13.923561        18.504029            0.752           0.452
L2.jp_i           -494.675878       700.243155           -0.706           0.480
L2.n225              0.055777         0.041768            1.335           0.182
L3.tokyo            -0.603774         0.228647           -2.641           0.008
L3.jp_gdp           -0.010116         0.005255           -1.925           0.054
L3.jp_unemp        310.757400       256.745433            1.210           0.226
L3.oil               8.644184         4.060182            2.129           0.033
L3.usdjpy            0.487636        18.475337            0.026           0.979
L3.jp_i            726.126100       704.949349            1.030           0.303
L3.n225              0.017197         0.041857            0.411           0.681
L4.tokyo            -0.161941         0.231980           -0.698           0.485
L4.jp_gdp           -0.002818         0.005220           -0.540           0.589
L4.jp_unemp         43.657383       257.336541            0.170           0.865
L4.oil               9.373969         3.973729            2.359           0.018
L4.usdjpy            8.148560        18.379822            0.443           0.658
L4.jp_i            474.499466       707.855437            0.670           0.503
L4.n225              0.039663         0.041887            0.947           0.344
L5.tokyo             0.219571         0.231799            0.947           0.344
L5.jp_gdp           -0.010153         0.005151           -1.971           0.049
L5.jp_unemp         32.473709       257.282258            0.126           0.900
L5.oil               2.475759         3.901425            0.635           0.526
L5.usdjpy           -4.109719        18.480543           -0.222           0.824
L5.jp_i            156.671912       709.463970            0.221           0.825
L5.n225             -0.012168         0.042202           -0.288           0.773
L6.tokyo            -0.225657         0.233164           -0.968           0.333
L6.jp_gdp            0.000866         0.005192            0.167           0.868
L6.jp_unemp       -266.019302       257.914671           -1.031           0.302
L6.oil               3.083201         3.883020            0.794           0.427
L6.usdjpy          -10.221159        18.467330           -0.553           0.580
L6.jp_i           1155.313525       710.037668            1.627           0.104
L6.n225             -0.047112         0.042551           -1.107           0.268
L7.tokyo             0.549556         0.233543            2.353           0.019
L7.jp_gdp           -0.002749         0.005142           -0.535           0.593
L7.jp_unemp        -44.033964       257.473150           -0.171           0.864
L7.oil              -4.393678         3.856305           -1.139           0.255
L7.usdjpy            9.101730        18.304060            0.497           0.619
L7.jp_i           -536.756282       710.885541           -0.755           0.450
L7.n225             -0.053393         0.042831           -1.247           0.213
L8.tokyo            -0.015429         0.233052           -0.066           0.947
L8.jp_gdp            0.013767         0.005109            2.695           0.007
L8.jp_unemp        -88.564279       256.639139           -0.345           0.730
L8.oil               4.831424         3.881351            1.245           0.213
L8.usdjpy            6.812512        18.358529            0.371           0.711
L8.jp_i           -683.930916       715.459399           -0.956           0.339
L8.n225             -0.068080         0.043018           -1.583           0.114
L9.tokyo             0.280374         0.232310            1.207           0.227
L9.jp_gdp           -0.013848         0.005045           -2.745           0.006
L9.jp_unemp       -185.663043       256.479776           -0.724           0.469
L9.oil               6.733802         3.896201            1.728           0.084
L9.usdjpy           12.014858        18.315814            0.656           0.512
L9.jp_i           1965.663760       713.736977            2.754           0.006
L9.n225             -0.046882         0.042732           -1.097           0.273
L10.tokyo           -0.028731         0.231923           -0.124           0.901
L10.jp_gdp          -0.000551         0.004987           -0.111           0.912
L10.jp_unemp      -101.278236       257.402649           -0.393           0.694
L10.oil             -1.426188         3.894837           -0.366           0.714
L10.usdjpy         -28.280815        18.458108           -1.532           0.125
L10.jp_i          1953.699449       719.826686            2.714           0.007
L10.n225             0.022146         0.043015            0.515           0.607
L11.tokyo            0.520901         0.231093            2.254           0.024
L11.jp_gdp           0.002547         0.004883            0.522           0.602
L11.jp_unemp       170.754318       257.328690            0.664           0.507
L11.oil             -6.269520         3.862057           -1.623           0.105
L11.usdjpy           7.598052        18.348852            0.414           0.679
L11.jp_i          -529.693089       719.818450           -0.736           0.462
L11.n225            -0.020526         0.042970           -0.478           0.633
L12.tokyo           -0.107131         0.233777           -0.458           0.647
L12.jp_gdp          -0.011385         0.004869           -2.338           0.019
L12.jp_unemp      -341.823974       257.122585           -1.329           0.184
L12.oil             -1.642383         3.855638           -0.426           0.670
L12.usdjpy           7.321627        18.436722            0.397           0.691
L12.jp_i           141.746139       721.315875            0.197           0.844
L12.n225            -0.001402         0.043348           -0.032           0.974
L13.tokyo            0.143531         0.232964            0.616           0.538
L13.jp_gdp          -0.000897         0.004792           -0.187           0.851
L13.jp_unemp       109.576253       257.122747            0.426           0.670
L13.oil              3.726541         3.822281            0.975           0.330
L13.usdjpy          -0.884042        18.230209           -0.048           0.961
L13.jp_i           778.532216       724.392554            1.075           0.282
L13.n225             0.051378         0.043295            1.187           0.235
L14.tokyo            0.229670         0.233203            0.985           0.325
L14.jp_gdp          -0.003068         0.006000           -0.511           0.609
L14.jp_unemp       283.704127       259.312813            1.094           0.274
L14.oil              6.768652         3.738361            1.811           0.070
L14.usdjpy         -37.076320        18.057659           -2.053           0.040
L14.jp_i           463.035285       723.335925            0.640           0.522
L14.n225            -0.010953         0.042996           -0.255           0.799
L15.tokyo            0.282975         0.234117            1.209           0.227
L15.jp_gdp          -0.000973         0.006234           -0.156           0.876
L15.jp_unemp      -202.843029       259.850802           -0.781           0.435
L15.oil              3.040779         3.437488            0.885           0.376
L15.usdjpy          13.924575        17.647338            0.789           0.430
L15.jp_i           -96.019986       719.177157           -0.134           0.894
L15.n225            -0.035308         0.042159           -0.837           0.402
===============================================================================

Correlation matrix of residuals
               tokyo    jp_gdp  jp_unemp       oil    usdjpy      jp_i      n225
tokyo       1.000000  0.007937 -0.089687  0.073427  0.111157  0.114727  0.393764
jp_gdp      0.007937  1.000000  0.076859 -0.018946 -0.028342  0.003233  0.076050
jp_unemp   -0.089687  0.076859  1.000000  0.001843 -0.024381  0.032169 -0.081158
oil         0.073427 -0.018946  0.001843  1.000000  0.067905  0.024838  0.176879
usdjpy      0.111157 -0.028342 -0.024381  0.067905  1.000000  0.321144  0.390177
jp_i        0.114727  0.003233  0.032169  0.024838  0.321144  1.000000  0.263747
n225        0.393764  0.076050 -0.081158  0.176879  0.390177  0.263747  1.000000


# Calculate yhat
yhat_var2_6 = var2_model6.forecast(var_model6.endog, steps=len(test_diff6))


# clean up yhat
df_yhat_var2_6 = pd.DataFrame(yhat_var2_6)
df_yhat_var2_6.index = test_diff6.index
df_yhat_var2_6.columns = test_diff6.columns
df_yhat_var2_6


# Recover first order differencing
df_pred_var2_6 = pd.concat([tokyo_6[tokyo_6.index==pd.datetime(2020,12,30)], df_yhat_var2_6], axis=0).cumsum()
df_pred_var2_6 = df_pred_var2_6[df_pred_var2_6.index!=pd.datetime(2020,12,30)]

y_pred_var2_6 = df_pred_var2_6["tokyo"]


fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
y_pred_var2_6.plot(ax=ax, label="VAR(15) with Oil, N225, Unemployement, GDP, USD-JPY", linestyle="dashed")
plt.legend()
plt.show()


var2_metrics6 = calc_metrics(y_test, y_pred_var2_6, return_dict=True)

Test Error Metrics
MAE: 148.0882
MSE: 32951.911
MAPE: 0.0711
sMAPE: 0.0676
MASE: -6.363


y_train = tokyo_gas[tokyo_gas.index.year!=2021]
y_test = tokyo_gas[tokyo_gas.index.year==2021]


# Convert y_train into Prophet-suitable format
y_train_p = pd.DataFrame(y_train)
y_train_p = y_train_p.reset_index().rename(columns={"Tokyo Gas":"y", "Date":"ds"})

# Convert y_test into Prophet-suitable format
y_test_p = pd.DataFrame(y_test)
y_test_p = y_test_p.reset_index().rename(columns={"Tokyo Gas":"y", "Date":"ds"})
y_test_p.size
y_train_p.size

1950


from fbprophet.plot import plot_plotly
from fbprophet import Prophet

# Train model with default parameter
p_model_1 = Prophet()
p_model_1.fit(y_train_p)

INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.

Initial log joint probability = -4.56358

<fbprophet.forecaster.Prophet at 0x7fe86cda90a0>

    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
      99          2748     0.0223508       667.786           1           1      120   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     199        2778.9    0.00948636       248.657      0.3866           1      231   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     299       2795.37    0.00321743       249.765           1           1      348   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     399       2804.08    0.00501663        280.05           1           1      465   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     499       2813.61    0.00319059       135.081           1           1      588   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     564       2818.53   0.000112124       213.617     5.2e-07       0.001      721  LS failed, Hessian reset 
     599        2822.4   0.000534906       113.517      0.7184      0.7184      761   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     699       2826.52   0.000647731       172.269           1           1      881   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     799       2829.72    0.00656521       436.282      0.4663      0.4663      997   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     803       2830.42    0.00074163       227.104   2.257e-06       0.001     1035  LS failed, Hessian reset 
     899       2833.93    0.00192072       132.104      0.2893           1     1148   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     996       2834.62   0.000100227       186.067   6.925e-07       0.001     1317  LS failed, Hessian reset 
     999       2834.64   0.000138779       109.043           1           1     1320   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1099       2834.97    0.00151381       114.104           1           1     1457   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1199       2836.65   0.000712144       179.669      0.2192      0.2192     1582   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1299       2837.25   0.000516239       82.9866      0.2651      0.6977     1702   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1399       2837.51   0.000653147       105.857      0.4754      0.4754     1826   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1499        2839.7    0.00734293       196.625           1           1     1949   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1599       2840.47     0.0025426       98.8108           1           1     2076   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1644       2840.61   2.15635e-05       66.5771   2.641e-07       0.001     2173  LS failed, Hessian reset 
    1678       2840.61   1.63198e-07       55.8203      0.2367           1     2217   
Optimization terminated normally: 
  Convergence detected: relative gradient magnitude is below tolerance


# Create future_data dataframe
future_data = p_model_1.make_future_dataframe(periods=len(y_test_p), freq='D')


# Make prediction
p_result_1 = p_model_1.predict(future_data)
p_result_1.head(3)


# Calculate predicted values (for test data)
p_pred_1 = p_result_1["yhat"][len(y_train):]
p_pred_1.index = y_test.index

# Display result
fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
p_pred_1.plot(ax=ax, label="Prediction", linestyle="dashed")
ax.set_title("Prophet (default setting)")
plt.legend()
plt.show()


prophet1_metrics = calc_metrics(y_test, p_pred_1, return_dict=True)

Test Error Metrics
MAE: 197.3705
MSE: 56943.7882
MAPE: 0.0943
sMAPE: 0.0886
MASE: -8.4805


# Add external regressor 
y_train_p_toyko = y_train_p.copy()
y_train_p_toyko["oil"] = tokyo_gas_m["oil"].values[:len(y_train_p_toyko)]
y_train_p_toyko["n225"] = tokyo_gas_m["n225"].values[:len(y_train_p_toyko)]


# Train model with default parameter
p_model_2 = Prophet()
p_model_2.add_regressor("oil")
p_model_2.add_regressor("n225")
p_model_2.fit(y_train_p_toyko)

INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.

<fbprophet.forecaster.Prophet at 0x7f31fec13410>


# Create future_data dataframe
future_data_toyko = p_model_2.make_future_dataframe(periods=len(y_test_p), freq='D')
future_data_toyko["oil"] = tokyo_gas_m["oil"].values
future_data_toyko["n225"] = tokyo_gas_m["n225"].values
future_data_toyko.head(2)


# Make prediction
p_result_2 = p_model_2.predict(future_data_toyko)
p_result_2.head(3)


# Calculate fitted values (for training data)
p_fitted_2 = p_result_2["yhat"][:len(y_train)]
p_fitted_2.index = y_train.index


# Calculate predicted values (for test data)
p_pred_2 = p_result_2["yhat"][len(y_train):]
p_pred_2.index = y_test.index

# Display result
fig, ax = plt.subplots(figsize=(16,5))
y_train.plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
p_pred_2.plot(ax=ax, label="Prediction", linestyle="dashed")
ax.set_title("Prophet with External Regressor")
plt.legend()
plt.show()


prophet2_metrics = calc_metrics(y_test, p_pred_2, return_dict=True)

Test Error Metrics
MAE: 120.3906
MSE: 20752.0242
MAPE: 0.0569
sMAPE: 0.0551
MASE: -5.1729


df_train = tokyo_gas_weekly[:-23]
df_test = tokyo_gas_weekly[-23:]


# Convert y_train into Prophet-suitable format
y_train_p = pd.DataFrame(df_train)
y_train_p = y_train_p.reset_index().rename(columns={"Tokyo Gas":"y", "Date":"ds"})

# Convert y_test into Prophet-suitable format
y_test_p = pd.DataFrame(df_test)
y_test_p = y_test_p.reset_index().rename(columns={"Tokyo Gas":"y", "Date":"ds"})
y_train_p.head(2)


from fbprophet.plot import plot_plotly
from fbprophet import Prophet

# Train model with default parameter
prophet_uni = Prophet()
prophet_uni.fit(y_train_p)

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.

<fbprophet.forecaster.Prophet at 0x7f31feb230d0>


# Create future_data dataframe
future_data = prophet_uni.make_future_dataframe(periods=len(y_test_p), freq='W')


# Make prediction
result_prophet_uni = prophet_uni.predict(future_data)
result_prophet_uni.head(3)


df_train = weekly_m[:-23]
df_test = weekly_m[-23:]
# Convert y_train into Prophet-suitable format
y_train_p = pd.DataFrame(df_train)
y_train_p = y_train_p.reset_index().rename(columns={"Tokyo Gas":"y", "Date":"ds"})

# Convert y_test into Prophet-suitable format
y_test_p = pd.DataFrame(df_test)
y_test_p = y_test_p.reset_index().rename(columns={"Tokyo Gas":"y", "Date":"ds"})


def run_prophet_(_list, train_y_p=y_train_p, test_y=y_test, df_merged=weekly_m):
    """
    Needs following inputs
    - _list: column names used as external regressors
    - train_y_p: y_train with prophet suitable format ('ds' and 'y')
    - test_y: y_test wiht normal format (length and index are needed)
    - df_merged: whole data (train+test) with external regressors
    """
    # Create df with external regressor
    y_train = train_y_p.copy()
    for c in _list:
        y_train[c] = df_merged[c].values[:len(y_train)]

    # Train model with default parameter
    prophet_model = Prophet()
    for c in _list:
        prophet_model.add_regressor(c)
    prophet_model.fit(y_train)

    # Create future_data dataframe
    future_data = prophet_model.make_future_dataframe(periods=len(test_y), freq='W')
    for c in _list:
        future_data[c] = df_merged[c].values
    
    # Make prediction
    prophet_result = prophet_model.predict(future_data)

    # Extract y_pred for test data
    pred_prophet = prophet_result["yhat"][len(y_train):]
    pred_prophet.index = test_y.index

    # Return modle, result, predicted values
    return prophet_model, prophet_result, pred_prophet


# With all regressors
prophet_all, result_prophet_all, pred_prophet_all = run_prophet_(_list=['jp_gdp', 'jp_unemp', 'oil', 'usdjpy', 'jp_i', 'n225'])

# Print result
print("Prophet (default) / all")
make_plot(y_train, y_test, pred_prophet_all, "Prophet (default) / all")
metrics_prophet_all = calc_metrics(y_test, pred_prophet_all, return_dict=True)

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.

Prophet (default) / all

Test Error Metrics
MAE: 106.9358
MSE: 13783.4934
MAPE: 0.0516
sMAPE: 0.0532
MASE: -0.9018


# Run Prophet
prophet_n225, result_prophet_n225, pred_prophet_n225 = run_prophet_(_list=['n225'])

# Print result
print("Prophet (default) / n225")
make_plot(y_train, y_test, pred_prophet_n225, "Prophet (default) / n225")
metrics_prophet_n225 = calc_metrics(y_test, pred_prophet_n225, return_dict=True)

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.

Prophet (default) / n225

Test Error Metrics
MAE: 111.7085
MSE: 18302.6546
MAPE: 0.0554
sMAPE: 0.0533
MASE: -0.9421


# Run Prophet
prophet_oilusdjpy, result_prophet_oilusdjpy, pred_prophet_oilusdjpy = run_prophet_(_list=['oil', 'usdjpy'])

# Print result
print("Prophet (default) / oil & USDJPY")
make_plot(y_train, y_test, pred_prophet_oilusdjpy, "Prophet (default) / oil & USDJPY")
metrics_prophet_oilusdjpy = calc_metrics(y_test, pred_prophet_oilusdjpy, return_dict=True)

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.

Prophet (default) / oil & USDJPY

Test Error Metrics
MAE: 113.8575
MSE: 18311.7282
MAPE: 0.0565
sMAPE: 0.0543
MASE: -0.9602


# Run Prophet
prophet_gdpunemp, result_prophet_gdpunemp, pred_prophet_gdpunemp = run_prophet_(_list=['jp_gdp', 'jp_unemp'])

# Print result
print("Prophet (default) / GDP & Unemp")
make_plot(y_train, y_test, pred_prophet_gdpunemp, "Prophet (default) / GDP & Unemp")
metrics_prophet_gdpunemp = calc_metrics(y_test, pred_prophet_gdpunemp, return_dict=True)

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.

Prophet (default) / GDP & Unemp

Test Error Metrics
MAE: 98.772
MSE: 12537.1325
MAPE: 0.0487
sMAPE: 0.0474
MASE: -0.833


df_tokyo = pd.Series(fitted_data, index = tokyo_gas.index)
df_tokyo = pd.DataFrame(df_tokyo).reset_index()
df_tokyo['ds'] = df_tokyo['Date']
df_tokyo = df_tokyo.drop(['Date'], axis = 1)
df_tokyo['y'] = df_tokyo[0]
df_tokyo = df_tokyo.drop([0], axis = 1)


train = df_tokyo.iloc[:int(len(df_tokyo)*0.75)]
test = df_tokyo.iloc[int(len(df_tokyo)*0.75):]


pmodel = Prophet()
pmodel.fit(train)

INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.

Initial log joint probability = -16.8576

<fbprophet.forecaster.Prophet at 0x7fe86cda9e80>

    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
      99        1747.4    0.00611402       245.253      0.3515           1      125   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     152       1755.75   0.000645741       115.432   2.407e-06       0.001      233  LS failed, Hessian reset 
     199       1757.79   0.000744222       66.6534          10           1      296   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     299       1760.68   0.000414647       87.8548      0.9737      0.9737      427   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     367       1762.58   0.000476129       139.536   6.199e-06       0.001      547  LS failed, Hessian reset 
     399       1763.72    5.7492e-05       61.0545      0.2352      0.2352      585   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     427       1763.91   0.000326365       100.032   2.799e-06       0.001      667  LS failed, Hessian reset 
     485       1764.03   0.000532719       82.8289   6.901e-06       0.001      784  LS failed, Hessian reset 
     499       1764.05   8.24827e-06       66.2096      0.2261      0.2261      803   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     524       1764.06   4.71895e-05       69.5702     5.3e-07       0.001      886  LS failed, Hessian reset 
     549       1764.07   2.23388e-07       70.0129      0.2742           1      916   
Optimization terminated normally: 
  Convergence detected: relative gradient magnitude is below tolerance


modeltuned = Prophet(changepoint_prior_scale=0.5, seasonality_prior_scale=0.01)
modeltuned.fit(train)

INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.

Initial log joint probability = -16.8576

<fbprophet.forecaster.Prophet at 0x7fe8cd030d00>

    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
      99       1923.63     0.0206014       348.146           1           1      123   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     199       2121.59     0.0102148       622.397      0.6409      0.6409      230   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     299       2139.48     0.0172466       202.801           1           1      347   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     399       2168.27     0.0327547       605.706     0.06411           1      457   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     499       2191.91    0.00680939       108.276           1           1      565   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     599       2200.09     0.0240781       199.207           1           1      672   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     699       2210.33   0.000585984       77.6127           1           1      784   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     799       2212.75    0.00891449       160.465      0.4812           1      890   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     899       2215.22     0.0202873       95.1593           1           1     1002   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
     999       2219.94    0.00903165       108.131           1           1     1119   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1099       2225.69    0.00814579       54.3188           1           1     1229   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1199       2228.64     0.0102898       67.6323           1           1     1349   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1299       2230.32    0.00104789       30.7275           1           1     1463   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1399       2232.04     0.0164327       26.0938           1           1     1572   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1499       2232.59   0.000786256       16.9541           1           1     1685   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1599       2233.11    0.00202475       92.7398      0.5167      0.5167     1801   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1699       2233.31     0.0149236       64.4038           1           1     1919   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1703       2233.34   9.44778e-05       50.4146    3.28e-06       0.001     1965  LS failed, Hessian reset 
    1799       2233.59    0.00020531       37.6313      0.4755      0.4755     2075   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1822       2233.63   3.43194e-05       22.9839   7.485e-07       0.001     2147  LS failed, Hessian reset 
    1899       2233.78    0.00047106       11.6668      0.7269      0.7269     2230   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    1999       2234.31      0.051291       127.772           1           1     2343   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    2099       2235.47    0.00133817       26.5849           1           1     2456   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    2120       2235.51   4.71743e-05       26.5766   3.706e-06       0.001     2522  LS failed, Hessian reset 
    2199       2235.57   0.000739277       16.7006           1           1     2615   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    2299        2235.9    0.00175838       41.3283           1           1     2734   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    2399        2236.1     0.0166701       11.5143           1           1     2846   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    2499       2236.25   0.000442497       53.7199     0.04056           1     2967   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    2565        2236.3   1.67164e-05       13.4866   1.126e-06       0.001     3086  LS failed, Hessian reset 
    2599       2236.31   3.58674e-05       5.48813           1           1     3133   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    2687       2236.44   0.000108085       78.4374   1.081e-06       0.001     3293  LS failed, Hessian reset 
    2699       2236.48   0.000214724        19.993           1           1     3305   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    2769       2236.53   4.04011e-05       12.3104   3.377e-06       0.001     3424  LS failed, Hessian reset 
    2799       2236.53   6.03413e-05       11.8028       0.661       0.661     3463   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    2823       2236.54   9.50755e-06       7.72469   1.082e-06       0.001     3537  LS failed, Hessian reset 
    2899       2236.55    5.7479e-05       7.98887      0.3813           1     3637   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    2999       2236.61    0.00412434       23.8031      0.6302      0.6302     3751   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    3099       2236.69   0.000147939       9.52879      0.5841           1     3866   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    3106       2236.69   1.35913e-05       10.5721   1.554e-06       0.001     3912  LS failed, Hessian reset 
    3199       2236.71    0.00103113        10.658      0.6586      0.6586     4026   
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
    3212       2236.71   1.00566e-05       7.93525   1.339e-06       0.001     4079  LS failed, Hessian reset 
    3232       2236.71   5.81152e-06       4.82531   1.038e-06       0.001     4148  LS failed, Hessian reset 
    3244       2236.71   5.86663e-06        4.3788      0.2883           1     4162   
Optimization terminated normally: 
  Convergence detected: relative gradient magnitude is below tolerance


future_data = modeltuned.make_future_dataframe(periods=len(test), freq='d')


forecast_data = modeltuned.predict(future_data)


residual_pm = train['y'] - forecast_data['yhat'][:900]


residual_pm.plot()
plt.title('Prophet Residual Plot')
plt.show()


residual_pm.hist()
plt.title('Prophet Residual Histogram')
plt.show()


p = plot_acf(residual_pm, lags=40, title='Prophet Residual Autocorrelation Plot')


sm.stats.acorr_ljungbox(residual_pm, lags=[10], return_df=True, boxpierce=True)


forecast_data_exp = pd.concat([
    forecast_data['ds'],
    inv_boxcox(forecast_data['yhat'], fitted_lambda)],axis=1)


tokyo_gas1 = pd.DataFrame(data = tokyo_gas).reset_index()


tokyo_gas1['ds'] = tokyo_gas1['Date']


tokyo_gas1 = tokyo_gas1.drop(['Date'], axis = 1)


tokyo_gas1['y'] = tokyo_gas1['Tokyo Gas']


tokyo_gas1 = tokyo_gas1.drop(['Tokyo Gas'], axis = 1)


tokyo_gas1['ds'] = pd.to_datetime(tokyo_gas1['ds'])
forecast_data_exp['ds'] = pd.to_datetime(forecast_data_exp['ds'])
comb = pd.merge_asof(forecast_data_exp[['ds','yhat']], tokyo_gas1[['ds','y']], on=['ds']).set_index('ds')


train_comb, test_comb = comb[comb.index<test['ds'].min()], comb[comb.index>=test['ds'].min()]


Prophet_TRAIN_MAE = mean_absolute_error(train_comb['y'], train_comb['yhat'])
Prophet_TRAIN_MSE = mean_squared_error(train_comb['y'], train_comb['yhat'])
Prophet_TRAIN_MAPE = mean_absolute_percentage_error(train_comb['y'], train_comb['yhat'], symmetric=False)
Prophet_TRAIN_SMAPE = mean_absolute_percentage_error(train_comb['y'], train_comb['yhat'])


print(f'Prophet TRAIN MAE: {Prophet_TRAIN_MAE}')
print(f'Prophet TRAIN MSE: {Prophet_TRAIN_MSE}')
print(f'Prophet TRAIN MAPE: {Prophet_TRAIN_MAPE}')
print(f'Prophet TRAIN SMAPE: {Prophet_TRAIN_SMAPE}')

Prophet TRAIN MAE: 48.14927362512074
Prophet TRAIN MSE: 4128.805761297893
Prophet TRAIN MAPE: 0.01820474440062813
Prophet TRAIN SMAPE: 0.01813276953161715


train_comb['y'].plot(color = 'blue', figsize=(15, 10))
test_comb['yhat'].plot(color='red')
test_comb['y'].plot(color = 'black')
plt.title('Propohet Model')
plt.show()


test_comb['yhat'].plot(color='red', figsize=(15, 10))
test_comb['y'].plot(color = 'black')
plt.title('Propohet Model Predictive Performance')
plt.show()


Prophet_TEST_MAE = mean_absolute_error(test_comb['y'], test_comb['yhat'])
Prophet_TEST_MSE = mean_squared_error(test_comb['y'], test_comb['yhat'])
Prophet_TEST_MAPE = mean_absolute_percentage_error(test_comb['y'], test_comb['yhat'], symmetric=False)
Prophet_TEST_SMAPE = mean_absolute_percentage_error(test_comb['y'], test_comb['yhat'])

/usr/local/lib/python3.7/dist-packages/sktime/performance_metrics/forecasting/_functions.py:1548: FutureWarning: In the percentage error metric functions the default argument symmetric=True is changing to symmetric=False in v0.12.0.
  FutureWarning,
/usr/local/lib/python3.7/dist-packages/sktime/performance_metrics/forecasting/_functions.py:1548: FutureWarning: In the percentage error metric functions the default argument symmetric=True is changing to symmetric=False in v0.12.0.
  FutureWarning,


print(f'Prophet TEST MAE: {Prophet_TEST_MAE}')
print(f'Prophet TEST MSE: {Prophet_TEST_MSE}')
print(f'Prophet TEST MAPE: {Prophet_TEST_MAPE}')
print(f'Prophet TEST SMAPE: {Prophet_TEST_SMAPE}')

Prophet TEST MAE: 174.70018620167997
Prophet TEST MSE: 49763.55046425741
Prophet TEST MAPE: 0.07399878601699326
Prophet TEST SMAPE: 0.07858572220829031


fitted_data, fitted_lambda = stats.boxcox(tokyo_gas)


df_tokyo = pd.Series(fitted_data, index = tokyo_gas.index)


adf_kpss(df_tokyo)

stationarity from ADF test: False
stationarity from KPSS test('c'): False
stationarity from KPSS test('ct'): False


y_train, y_test = temporal_train_test_split(df_tokyo)


y_train_nonseasdiff = y_train.diff(1).dropna()


main5 = df.copy().loc[df["SecuritiesCode"].isin([9501, 9503, 9531, 9532, 5020]), ["Date", "SecuritiesCode", "Close", "Name", "Category"]]
main5.loc[main5["Name"]=="ENEOS Holdings,Inc.", "Name"] = "ENEOS"
main5.loc[main5["Name"]=="Tokyo Electric Power Company Holdings,Incorporated", "Name"] = "Tokyo Electric Power"
main5.loc[main5["Name"]=="The Kansai Electric Power Company,Incorporated", "Name"] = "Kansai Electric Power"
main5.loc[main5["Name"]=="TOKYO GAS CO.,LTD.", "Name"] = "Tokyo Gas"
main5.loc[main5["Name"]=="OSAKA GAS CO.,LTD.", "Name"] = "Osaka Gas"


main5["Adjusted Close"] = main5["Close"]
main5.loc[(main5["SecuritiesCode"].isin([9531, 9532])) & (main5["Date"] < dt.datetime(2017,9,27)), "Adjusted Close"] = main5.loc[(main5["SecuritiesCode"].isin([9531, 9532])) & (main5["Date"] < dt.datetime(2017,9,27)), "Adjusted Close"]*5


tokyo_gas = main5.loc[main5["Name"]=="Tokyo Gas", "Adjusted Close"].dropna()


dataset = tokyo_gas[:900]


dataset = dataset.to_numpy()


def split_sequence(sequence, n_steps):
	X, y = list(), list()
	for i in range(len(sequence)):
		end_ix = i + n_steps
		if end_ix > len(sequence)-1:
			break
		seq_x, seq_y = sequence[i:end_ix], sequence[end_ix]
		X.append(seq_x)
		y.append(seq_y)
	return np.array(X), np.array(y)


n_steps = 30
X, y = split_sequence(dataset, n_steps)


n_features = 1
X = X.reshape((X.shape[0], X.shape[1], n_features))


X.shape

(870, 30, 1)


y.shape

(870,)


np.random.seed(42)
tf.random.set_seed(42)
model = keras.models.Sequential()
model.add(keras.layers.LSTM(50, activation='relu', return_sequences=True, input_shape=(n_steps, n_features)))
model.add(keras.layers.LSTM(50, activation='relu'))
model.add(keras.layers.Dense(1, activation="relu"))
model.compile(optimizer='adam', loss='mse')
history = model.fit(X, y, epochs=50, verbose=0)

WARNING:tensorflow:Layer lstm_8 will not use cuDNN kernels since it doesn't meet the criteria. It will use a generic GPU kernel as fallback when running on GPU.

WARNING:tensorflow:Layer lstm_8 will not use cuDNN kernels since it doesn't meet the criteria. It will use a generic GPU kernel as fallback when running on GPU.

WARNING:tensorflow:Layer lstm_9 will not use cuDNN kernels since it doesn't meet the criteria. It will use a generic GPU kernel as fallback when running on GPU.

WARNING:tensorflow:Layer lstm_9 will not use cuDNN kernels since it doesn't meet the criteria. It will use a generic GPU kernel as fallback when running on GPU.


model.save("LSTM_model.h5")


keras.utils.plot_model(model, show_shapes=True)


pd.DataFrame(history.history).plot(figsize=(8, 5))
plt.grid(True)
plt.title('LSTM Learning Curve')
plt.show()


x_input = dataset[-30:]
x_input = x_input.reshape((1, n_steps, n_features))


x_input = dataset[-30:]
LSTM_pred = []
for i in range(0, 301):
  x_input_arr = x_input.reshape((1, n_steps, n_features))
  new_pred = model.predict(x_input_arr, verbose=0)
  LSTM_pred.append(new_pred[0][0])
  x_input = np.delete(x_input, 0)
  x_input = np.append(x_input, new_pred)


LSTM_pred = pd.Series(LSTM_pred, index = tokyo_gas.index[-301:])


tokyo_gas[:900].plot(color = 'blue', figsize=(15, 10))
LSTM_pred.plot(color='red')
tokyo_gas[-301:].plot(color = 'black')
plt.title('LSTM Model')
plt.show()


LSTM_pred.plot(color='red', figsize=(15, 10))
tokyo_gas[-301:].plot(color = 'black')
plt.title('LSTM Model Predictive Performance')
plt.show()


LSTM_TEST_MAE = mean_absolute_error(tokyo_gas[-301:], LSTM_pred)
LSTM_TEST_MSE = mean_squared_error(tokyo_gas[-301:], LSTM_pred)
LSTM_TEST_MAPE = mean_absolute_percentage_error(tokyo_gas[-301:], LSTM_pred, symmetric=False)
LSTM_TEST_SMAPE = mean_absolute_percentage_error(tokyo_gas[-301:], LSTM_pred)

/usr/local/lib/python3.7/dist-packages/sktime/performance_metrics/forecasting/_functions.py:1548: FutureWarning: In the percentage error metric functions the default argument symmetric=True is changing to symmetric=False in v0.12.0.
  FutureWarning,
/usr/local/lib/python3.7/dist-packages/sktime/performance_metrics/forecasting/_functions.py:1548: FutureWarning: In the percentage error metric functions the default argument symmetric=True is changing to symmetric=False in v0.12.0.
  FutureWarning,


print(f'LSTM TEST MAE: {LSTM_TEST_MAE}')
print(f'LSTM TEST MSE: {LSTM_TEST_MSE}')
print(f'LSTM TEST MAPE: {LSTM_TEST_MAPE}')
print(f'LSTM TEST SMAPE: {LSTM_TEST_SMAPE}')

LSTM TEST MAE: 88.87023723006645
LSTM TEST MSE: 14273.594674552101
LSTM TEST MAPE: 0.03885517634287059
LSTM TEST SMAPE: 0.03966203776120834


# Take average of each week
eneos_weekly = eneos.resample("W").mean()


# NA value in 2019-05-05 due to consecutive national holidays (called "Golden Week")
eneos_weekly[eneos_weekly.isna()]

Date
2019-05-05   NaN
Freq: W-SUN, Name: eneos, dtype: float64


# Fill NA with interpolation
eneos_weekly = eneos_weekly.interpolate()


# Check stationarity
create_plot_adf_kpss(eneos_weekly, "ENEOS_weekly")

ADF/KPSS tests for ENEOS_weekly (alpha=0.05):
stationarity from ADF test: False
stationarity from KPSS test('c'): False
stationarity from KPSS test('ct'): False


# Check seasonality: No seasonality
df_season = pd.DataFrame(eneos_weekly)
df_season["year"] = df_season.index.year
df_season["week"] = df_season.index.week

# Line plot
fig, ax = plt.subplots(figsize=(15,6))
sns.lineplot("week", "eneos", data=df_season, hue="year", ax=ax, legend=None)
ax.grid()
plt.show()


# Check stationarity for differenced data
create_plot_adf_kpss(eneos_weekly.diff().dropna(), "ENEOS_weekly_diff")

ADF/KPSS tests for ENEOS_weekly_diff (alpha=0.05):
stationarity from ADF test: True
stationarity from KPSS test('c'): True
stationarity from KPSS test('ct'): True


plot_acf_pacf(eneos_weekly.diff().dropna(), "ENEOS Weekly (diff(1))", lags=80)


# GDP
gdp_weekly = gdp_s.resample("W").mean().fillna(method="ffill")


# unemplyment rate
unemp_weekly = unemp_s.resample("W").mean().fillna(method="ffill")


# Oil Price
oil_weekly = oil_s.resample("W").mean()


# JPY/USD
usdjpy_weekly = usdjpy_s.resample("W").mean()


# Interest Rate (long-term)
interest_weekly = interest_s.resample("W").mean()


# Find NAs for interest_weekly
interest_weekly[interest_weekly.isna()]

Date
2019-05-05   NaN
Freq: W-SUN, Name: jp_i, dtype: float64


# Interpolation
interest_weekly = interest_weekly.interpolate()


# Nikkei 225 index
n225_weekly = n225_s.resample("W").mean()


# Find NAs
n225_weekly[n225_weekly.isna()]

Date
2019-05-05   NaN
Freq: W-SUN, Name: n225, dtype: float64


# Interpolation
n225_weekly = n225_weekly.interpolate()


# Merge data
weekly_m = pd.concat([eneos_weekly, gdp_weekly, unemp_weekly, oil_weekly, usdjpy_weekly, interest_weekly, n225_weekly], axis=1)

# Show rows with NAs => Need to fill jp_gdp (since last observation for gdp_weekly is for 2021-10-03)
weekly_m[weekly_m.isnull().any(axis=1)]


# Drop rows when "eneos" is NA 
weekly_m = weekly_m.dropna(subset=["eneos"])

# Show rows with NAs
weekly_m[weekly_m.isnull().any(axis=1)]


# Fill NAs for jp_gdp with forward fill
weekly_m["jp_gdp"] = weekly_m["jp_gdp"].fillna(method="ffill")

# Show rows with NAs
weekly_m[weekly_m.isnull().any(axis=1)]


# Plot external regressors
fig, axes = plt.subplots(2,3, figsize=(16,8), tight_layout=True)
axes_flat = [s for sublist in axes for s in sublist]
for i, c in enumerate(weekly_m.columns.difference(["eneos"])):
    weekly_m[c].plot(ax=axes_flat[i])
    axes_flat[i].set_title(c)
plt.show()


# Using data before June 2021 as training
df_train = weekly_m[:-23]
df_test = weekly_m[-23:]


df_train


df_test


# extract eneos sereis as y_train and y_test
y_train = df_train["eneos"]
y_test = df_test["eneos"]


# Make prediction with arima model from pmdarima
def predict_from_arima(arima_model, test_y, test_X=None):
    y_pred = arima_model.predict(n_periods=len(test_y), X=test_X)
    y_pred = pd.Series(y_pred)
    y_pred.index = test_y.index
    return y_pred


# Make plot fro training/test/prediction
def make_plot(train_y, test_y, pred_y, title):
    fig, ax = plt.subplots(figsize=(16,5))
    train_y.plot(ax=ax, label="Training")
    test_y.plot(ax=ax, label="Test", color="black")
    pred_y.plot(ax=ax, label=title, linestyle="dashed")
    plt.legend()
    plt.show()


# Function to run rolling fit
def rolling_arima3(train_y_raw, test_y_raw):

    # Series to store predicted values
    y_pred = pd.Series(name="eneos")

    # Set initial training / test data / prediction
    train_y = train_y_raw.copy()
    test_y = test_y_raw.copy()

    for i in range(len(test_y)):
        # Train ARIMA and make 1-step ahead forecast
        arima = auto_arima(train_y, start_p=0, d=1, start_q=0, seasonal=False)
        arima_order = arima.get_params()["order"]
        ypred = pd.Series(arima.predict(1), name="eneos", index=[test_y_raw.index[i]])

        # Store predicted value into y_pred
        y_pred = y_pred.append(ypred)

        # Add 1-step ahead true observation to train_y and drop first observation from train_y
        train_y = train_y.append(test_y[i:i+1])[1:]

        # Print progress      
        print(f"Index {i+1}: ARIMA{str(arima_order)} : Prediction: {ypred.index[0].strftime('%Y-%m-%d')} {ypred.values}")
    
    return y_pred


pred_airma_rolling_uni3 = rolling_arima3(y_train, y_test)

Index 1: ARIMA(0, 1, 1) : Prediction: 2021-07-04 [466.04885912]
Index 2: ARIMA(0, 1, 1) : Prediction: 2021-07-11 [469.12423017]
Index 3: ARIMA(0, 1, 1) : Prediction: 2021-07-18 [468.03096663]
Index 4: ARIMA(0, 1, 1) : Prediction: 2021-07-25 [474.18261045]
Index 5: ARIMA(0, 1, 1) : Prediction: 2021-08-01 [448.54126388]
Index 6: ARIMA(0, 1, 1) : Prediction: 2021-08-08 [463.53587825]
Index 7: ARIMA(0, 1, 1) : Prediction: 2021-08-15 [465.33062447]
Index 8: ARIMA(0, 1, 1) : Prediction: 2021-08-22 [467.25361844]
Index 9: ARIMA(0, 1, 1) : Prediction: 2021-08-29 [422.5013441]
Index 10: ARIMA(0, 1, 1) : Prediction: 2021-09-05 [421.83617573]
Index 11: ARIMA(0, 1, 1) : Prediction: 2021-09-12 [432.76519871]
Index 12: ARIMA(0, 1, 1) : Prediction: 2021-09-19 [450.75625216]
Index 13: ARIMA(0, 1, 1) : Prediction: 2021-09-26 [463.58074917]
Index 14: ARIMA(0, 1, 1) : Prediction: 2021-10-03 [459.25553856]
Index 15: ARIMA(0, 1, 1) : Prediction: 2021-10-10 [463.32435339]
Index 16: ARIMA(0, 1, 1) : Prediction: 2021-10-17 [451.7806552]
Index 17: ARIMA(0, 1, 1) : Prediction: 2021-10-24 [462.54864079]
Index 18: ARIMA(0, 1, 1) : Prediction: 2021-10-31 [468.53173626]
Index 19: ARIMA(0, 1, 1) : Prediction: 2021-11-07 [463.42066449]
Index 20: ARIMA(0, 1, 1) : Prediction: 2021-11-14 [461.65189994]
Index 21: ARIMA(0, 1, 1) : Prediction: 2021-11-21 [458.67311245]
Index 22: ARIMA(0, 1, 1) : Prediction: 2021-11-28 [439.93671082]
Index 23: ARIMA(0, 1, 1) : Prediction: 2021-12-05 [435.04550794]


print("Rolling ARIMA3 / No-exog")
make_plot(y_train, y_test, pred_airma_rolling_uni3, "Rolling ARIMA3 / No-exog")
metrics_airma_rolling_uni3 = calc_metrics(y_test, pred_airma_rolling_uni3, return_dict=True)

Rolling ARIMA3 / No-exog

Test Error Metrics
MAE: 7.7174
MSE: 120.645
MAPE: 0.0172
sMAPE: 0.0171
MASE: 10.232


# Function to run rolling fit
def rolling_arima4(train_y_raw, test_y_raw):

    # Series to store predicted values
    y_pred = pd.Series(name="eneos")

    # Set initial training / test data / prediction
    train_y = train_y_raw.copy()[-52:]
    test_y = test_y_raw.copy()

    for i in range(len(test_y)):
        # Train ARIMA and make 1-step ahead forecast
        arima = auto_arima(train_y, start_p=0, d=1, start_q=0, seasonal=False)
        arima_order = arima.get_params()["order"]
        ypred = pd.Series(arima.predict(1), name="eneos", index=[test_y_raw.index[i]])

        # Store predicted value into y_pred
        y_pred = y_pred.append(ypred)

        # Add 1-step ahead true observation to train_y and drop first observation from train_y
        train_y = train_y.append(test_y[i:i+1])[1:]

        # Print progress      
        print(f"Index {i+1}: ARIMA{str(arima_order)} : Prediction: {ypred.index[0].strftime('%Y-%m-%d')} {ypred.values}")
    
    return y_pred


pred_airma_rolling_uni4 = rolling_arima4(y_train, y_test)

Index 1: ARIMA(0, 1, 1) : Prediction: 2021-07-04 [465.92946759]
Index 2: ARIMA(0, 1, 1) : Prediction: 2021-07-11 [469.25236729]
Index 3: ARIMA(0, 1, 1) : Prediction: 2021-07-18 [467.96385521]
Index 4: ARIMA(1, 1, 0) : Prediction: 2021-07-25 [474.3483901]
Index 5: ARIMA(1, 1, 0) : Prediction: 2021-08-01 [448.3256459]
Index 6: ARIMA(1, 1, 0) : Prediction: 2021-08-08 [462.49101024]
Index 7: ARIMA(1, 1, 0) : Prediction: 2021-08-15 [466.35811465]
Index 8: ARIMA(1, 1, 0) : Prediction: 2021-08-22 [467.42946451]
Index 9: ARIMA(0, 1, 0) : Prediction: 2021-08-29 [431.86]
Index 10: ARIMA(1, 1, 0) : Prediction: 2021-09-05 [419.0842712]
Index 11: ARIMA(0, 1, 1) : Prediction: 2021-09-12 [432.80907358]
Index 12: ARIMA(0, 1, 1) : Prediction: 2021-09-19 [450.94037173]
Index 13: ARIMA(1, 1, 0) : Prediction: 2021-09-26 [465.10402167]
Index 14: ARIMA(0, 1, 1) : Prediction: 2021-10-03 [459.12547473]
Index 15: ARIMA(0, 1, 1) : Prediction: 2021-10-10 [463.45498001]
Index 16: ARIMA(0, 1, 1) : Prediction: 2021-10-17 [451.56225879]
Index 17: ARIMA(0, 1, 1) : Prediction: 2021-10-24 [462.65304672]
Index 18: ARIMA(0, 1, 1) : Prediction: 2021-10-31 [468.54404857]
Index 19: ARIMA(0, 1, 1) : Prediction: 2021-11-07 [463.38565373]
Index 20: ARIMA(0, 1, 1) : Prediction: 2021-11-14 [461.65000441]
Index 21: ARIMA(0, 1, 1) : Prediction: 2021-11-21 [458.64814947]
Index 22: ARIMA(0, 1, 1) : Prediction: 2021-11-28 [439.57177806]
Index 23: ARIMA(1, 1, 0) : Prediction: 2021-12-05 [433.7105553]


print("Rolling ARIMA4 / No-exog")
make_plot(y_train, y_test, pred_airma_rolling_uni4, "Rolling ARIMA4 / No-exog")
metrics_airma_rolling_uni4 = calc_metrics(y_test, pred_airma_rolling_uni4, return_dict=True)

Rolling ARIMA4 / No-exog

Test Error Metrics
MAE: 8.2791
MSE: 127.8672
MAPE: 0.0185
sMAPE: 0.0184
MASE: 10.9768


# Function to run rolling fit
def rolling_arimax3(exog_list, train_df=df_train, test_df=df_test, verbose=False):
    """
    Input:
        (1) exog_list: column names for external regressors
        (2) train_df: df_train
        (3) test_df: df for extracting index / exog for training
    Process:
        (1) Build model using auto_arima() and whole training data (eneos + external regressors)
        (2) Make one-step ahead prediction for external regressors using actual values available at the point of prediction
        (3) Use model from (1) and external regressors from (2) to make one-step ahead prediction for eneos
        (4) Store predicted eneos and predicted external regressors as training data
        (5) Repeat (1) through (4) over test data periods
    Outoput:
        - Prediction for Eneos (23-step ahead)
    """
    # Extract eneos from train/test df as train_y and test_y
    train_y = train_df.copy()["eneos"]
    test_y = test_df.copy()["eneos"]

    # Create df for external regressors (Use whole trainig data)
    df_X = train_df.copy()[exog_list]

    # Series to store predicted values
    y_pred = pd.Series(name="eneos")

    for i in range(test_df.shape[0]):
        # Create ARIMAX model using training eneos and external regressors (df_X)
        arimax = auto_arima(train_y, X=df_X, start_p=0, d=1, start_q=0, seasonal=False)
        arimax_order = arimax.get_params()["order"]

        # Create df for predicted external regressors
        df_pred_exog = pd.DataFrame(columns=exog_list, index=[test_df.index[i]])

        # Make one-step ahead forecast for external regressors
        for c in exog_list:
            arima_exog = auto_arima(df_X[c], start_p=0, d=1, start_q=0, seasonal=False)
            pred_exog = arima_exog.predict(n_periods=1)
            df_pred_exog[c] = pred_exog
        
        # Make prediction
        ypred = arimax.predict(n_periods=1, X=df_pred_exog)
        ypred = pd.Series(ypred, name="eneos", index=[test_df.index[i]])

        # Store predicted value into y_pred
        y_pred = y_pred.append(ypred)

        # Add 1-step ahead true observation to train_y and drop first observation from train_y
        train_y = train_y.append(test_y[i:i+1])[1:]

        # Add 1-step ahead true external regressors into df_X and drop first observation from df_X
        df_X = df_X.append(test_df.copy().iloc[i][exog_list])[1:]

        # Print progress
        if verbose:
            print(f"Index {i + 1}")
            print(f"     ARIMAX{str(arimax_order)} : Prediction: {ypred.index[0].strftime('%Y-%m-%d')} {ypred.values}")
            print("     One-step ahead forecast for External Regressors:")
            display(df_pred_exog)
    
    return y_pred


pred_rolling_arimax_all3 = rolling_arimax3(exog_list=['jp_gdp', 'jp_unemp', 'oil', 'usdjpy', 'jp_i', 'n225'], verbose=True)

Index 1
     ARIMAX(0, 1, 1) : Prediction: 2021-07-04 [465.91477323]
     One-step ahead forecast for External Regressors:

Index 2
     ARIMAX(0, 1, 1) : Prediction: 2021-07-11 [467.89726752]
     One-step ahead forecast for External Regressors:

Index 3
     ARIMAX(0, 1, 1) : Prediction: 2021-07-18 [467.33418279]
     One-step ahead forecast for External Regressors:

Index 4
     ARIMAX(0, 1, 1) : Prediction: 2021-07-25 [474.06311931]
     One-step ahead forecast for External Regressors:

Index 5
     ARIMAX(0, 1, 1) : Prediction: 2021-08-01 [450.19378469]
     One-step ahead forecast for External Regressors:

Index 6
     ARIMAX(0, 1, 1) : Prediction: 2021-08-08 [463.17176243]
     One-step ahead forecast for External Regressors:

Index 7
     ARIMAX(0, 1, 1) : Prediction: 2021-08-15 [464.46909374]
     One-step ahead forecast for External Regressors:

Index 8
     ARIMAX(0, 1, 1) : Prediction: 2021-08-22 [467.44840949]
     One-step ahead forecast for External Regressors:

Index 9
     ARIMAX(0, 1, 1) : Prediction: 2021-08-29 [425.91171047]
     One-step ahead forecast for External Regressors:

Index 10
     ARIMAX(0, 1, 1) : Prediction: 2021-09-05 [422.51938531]
     One-step ahead forecast for External Regressors:


print("Rolling ARIMAX3 / all exog")
make_plot(y_train, y_test, pred_rolling_arimax_all3, "Rolling ARIMAX3 / all exog")
metrics_rolling_arimax_all3 = calc_metrics(y_test, pred_rolling_arimax_all3, return_dict=True)

Rolling ARIMAX3 / all exog

Test Error Metrics
MAE: 8.0231
MSE: 123.2682
MAPE: 0.0179
sMAPE: 0.0178
MASE: 10.6373


pred_rolling_arimax_n2253 = rolling_arimax3(exog_list=['n225'], verbose=False)


print("Rolling ARIMAX3 / n225")
make_plot(y_train, y_test, pred_rolling_arimax_n2253, "Rolling ARIMAX3 / n225")
metrics_rolling_arimax_n2253 = calc_metrics(y_test, pred_rolling_arimax_n2253, return_dict=True)

Rolling ARIMAX3 / n225

Test Error Metrics
MAE: 8.0718
MSE: 124.1081
MAPE: 0.0181
sMAPE: 0.0179
MASE: 10.7018


pred_rolling_arimax_oilusdjpy3 = rolling_arimax3(exog_list=['oil', 'usdjpy'], verbose=False)


print("Rolling ARIMAX3 / Oil & USDJPY")
make_plot(y_train, y_test, pred_rolling_arimax_oilusdjpy3, "Rolling ARIMAX3 / Oil & USDJPY")
metrics_rolling_arimax_oilusdjpy3 = calc_metrics(y_test, pred_rolling_arimax_oilusdjpy3, return_dict=True)

Rolling ARIMAX3 / Oil & USDJPY

Test Error Metrics
MAE: 7.8984
MSE: 122.567
MAPE: 0.0177
sMAPE: 0.0175
MASE: 10.472


pred_rolling_arimax_gdpunemp3 = rolling_arimax3(exog_list=['jp_gdp', 'jp_unemp'], verbose=False)


print("Rolling ARIMAX3 / GDP & Unemp")
make_plot(y_train, y_test, pred_rolling_arimax_gdpunemp3, "Rolling ARIMAX3 / GDP & Unemp")
metrics_rolling_arimax_gdpunemp3 = calc_metrics(y_test, pred_rolling_arimax_gdpunemp3, return_dict=True)

Rolling ARIMAX3 / GDP & Unemp

Test Error Metrics
MAE: 7.6359
MSE: 118.8654
MAPE: 0.0171
sMAPE: 0.0169
MASE: 10.1239


# Function to run rolling fit
def rolling_arimax4(exog_list, train_df=df_train, test_df=df_test, verbose=False):
    """
    ***** Rolling ARIMAX(3) uses whole training data, while Rolling ARIMAX(4) uses 52 latest values for prediction  *****
    Input:
        (1) exog_list: column names for external regressors
        (2) train_df: df_train
        (3) test_df: df for extracting index / exog for training
    Process:
        (1) Build model using auto_arima() and whole training data (eneos + external regressors / use only 52 latest values)
        (2) Make one-step ahead prediction for external regressors using actual values available at the point of prediction
        (3) Use model from (1) and external regressors from (2) to make one-step ahead prediction for eneos
        (4) Store predicted eneos and predicted external regressors as training data
        (5) Repeat (1) through (4) over test data periods
    Outoput:
        - Prediction for Eneos (23-step ahead)
    """
    # Extract eneos from train/test df as train_y and test_y (use last 52 values for train_y)
    train_y = train_df.copy()[-52:]["eneos"]
    test_y = test_df.copy()["eneos"]

    # Create df for external regressors (Use last 52 values)
    df_X = train_df.copy()[-52:][exog_list]

    # Series to store predicted values
    y_pred = pd.Series(name="eneos")

    for i in range(test_df.shape[0]):
        # Create ARIMAX model using training eneos and external regressors (df_X)
        arimax = auto_arima(train_y, X=df_X, start_p=0, d=1, start_q=0, seasonal=False)
        arimax_order = arimax.get_params()["order"]

        # Create df for predicted external regressors
        df_pred_exog = pd.DataFrame(columns=exog_list, index=[test_df.index[i]])

        # Make one-step ahead forecast for external regressors
        for c in exog_list:
            arima_exog = auto_arima(df_X[c], start_p=0, d=1, start_q=0, seasonal=False)
            pred_exog = arima_exog.predict(n_periods=1)
            df_pred_exog[c] = pred_exog
        
        # Make prediction
        ypred = arimax.predict(n_periods=1, X=df_pred_exog)
        ypred = pd.Series(ypred, name="eneos", index=[test_df.index[i]])

        # Store predicted value into y_pred
        y_pred = y_pred.append(ypred)

        # Add 1-step ahead true observation to train_y and drop first observation from train_y
        train_y = train_y.append(test_y[i:i+1])[1:]

        # Add 1-step ahead true external regressors into df_X and drop first observation from df_X
        df_X = df_X.append(test_df.copy().iloc[i][exog_list])[1:]

        # Print progress
        if verbose:
            print(f"Index {i + 1}")
            print(f"     ARIMAX{str(arimax_order)} : Prediction: {ypred.index[0].strftime('%Y-%m-%d')} {ypred.values}")
            print("     One-step ahead forecast for External Regressors:")
            display(df_pred_exog)
    
    return y_pred


pred_rolling_arimax_all4 = rolling_arimax4(exog_list=['jp_gdp', 'jp_unemp', 'oil', 'usdjpy', 'jp_i', 'n225'], verbose=True)

Index 1
     ARIMAX(0, 1, 0) : Prediction: 2021-07-04 [468.85475778]
     One-step ahead forecast for External Regressors:

Index 2
     ARIMAX(0, 1, 0) : Prediction: 2021-07-11 [470.37104768]
     One-step ahead forecast for External Regressors:

Index 3
     ARIMAX(0, 1, 0) : Prediction: 2021-07-18 [470.00972894]
     One-step ahead forecast for External Regressors:

Index 4
     ARIMAX(0, 1, 0) : Prediction: 2021-07-25 [474.63855928]
     One-step ahead forecast for External Regressors:

Index 5
     ARIMAX(0, 1, 0) : Prediction: 2021-08-01 [455.57135168]
     One-step ahead forecast for External Regressors:

Index 6
     ARIMAX(1, 1, 2) : Prediction: 2021-08-08 [463.54081244]
     One-step ahead forecast for External Regressors:

Index 7
     ARIMAX(0, 1, 1) : Prediction: 2021-08-15 [469.58547707]
     One-step ahead forecast for External Regressors:

Index 8
     ARIMAX(1, 1, 0) : Prediction: 2021-08-22 [468.58825959]
     One-step ahead forecast for External Regressors:

Index 9
     ARIMAX(1, 1, 2) : Prediction: 2021-08-29 [421.50703324]
     One-step ahead forecast for External Regressors:

Index 10
     ARIMAX(1, 1, 2) : Prediction: 2021-09-05 [418.42460147]
     One-step ahead forecast for External Regressors:


print("Rolling ARIMAX4 / all exog")
make_plot(y_train, y_test, pred_rolling_arimax_all4, "Rolling ARIMAX4 / all exog")
metrics_rolling_arimax_all4 = calc_metrics(y_test, pred_rolling_arimax_all4, return_dict=True)

Rolling ARIMAX4 / all exog

Test Error Metrics
MAE: 7.7303
MSE: 131.0375
MAPE: 0.0174
sMAPE: 0.0171
MASE: 10.2491


pred_rolling_arimax_n2254 = rolling_arimax4(exog_list=['n225'], verbose=False)


print("Rolling ARIMAX4 / n225")
make_plot(y_train, y_test, pred_rolling_arimax_n2254, "Rolling ARIMAX4 / n225")
metrics_rolling_arimax_n2254 = calc_metrics(y_test, pred_rolling_arimax_n2254, return_dict=True)

Rolling ARIMAX4 / n225

Test Error Metrics
MAE: 7.411
MSE: 127.3857
MAPE: 0.0166
sMAPE: 0.0164
MASE: 9.8258


pred_rolling_arimax_oilusdjpy4 = rolling_arimax4(exog_list=['oil', 'usdjpy'], verbose=False)


print("Rolling ARIMAX4 / Oil & USDJPY")
make_plot(y_train, y_test, pred_rolling_arimax_oilusdjpy4, "Rolling ARIMAX3 / Oil & USDJPY")
metrics_rolling_arimax_oilusdjpy4 = calc_metrics(y_test, pred_rolling_arimax_oilusdjpy4, return_dict=True)

Rolling ARIMAX4 / Oil & USDJPY

Test Error Metrics
MAE: 8.2142
MSE: 127.4794
MAPE: 0.0185
sMAPE: 0.0182
MASE: 10.8906


pred_rolling_arimax_gdpunemp4 = rolling_arimax4(exog_list=['jp_gdp', 'jp_unemp'], verbose=False)


print("Rolling ARIMAX4 / GDP & Unemp")
make_plot(y_train, y_test, pred_rolling_arimax_gdpunemp4, "Rolling ARIMAX4 / GDP & Unemp")
metrics_rolling_arimax_gdpunemp4 = calc_metrics(y_test, pred_rolling_arimax_gdpunemp4, return_dict=True)

Rolling ARIMAX4 / GDP & Unemp

Test Error Metrics
MAE: 8.084
MSE: 123.1674
MAPE: 0.0181
sMAPE: 0.0179
MASE: 10.718


# Library
from statsmodels.tsa.vector_ar.var_model import VAR

# Function to run VAR
def rolling_var(exog_list, train_diff_raw=df_train_diff, test_diff_raw=df_test_diff, train_raw=df_train, verbose=False):
    """
    Input:
        (1) exog_list: column names for external regressors
        (2) train_diff_raw: df_train_diff (differenced training data)
        (3) test_diff_raw: df for extracting index / exog for training
        (4) train_raw: df_train (non-differenced training data)
    Process:
        (1) Build model using VAR() with optimal order p in terms of AIC using whole differenced training data
        (2) Make one-step ahead prediction & Store predicted values
        (3) Add 1-step ahead true values into differenced training data and drop first observation from it
        (5) Repeat (1) through (3) over test data periods
    Outoput:
        - Prediction for Eneos (23-step ahead)
    """
    # Slice data by eneos and specified exog
    train_diff = train_diff_raw[["eneos"] + exog_list]
    test_diff = test_diff_raw[["eneos"] + exog_list]
    train = train_raw[["eneos"] + exog_list]

    # DF to store predicted values
    df_pred = pd.DataFrame(columns=train.columns)

    # Fit var model and make 1-step ahead prediction
    for i in range(test_diff.shape[0]):

        # Create instance
        var_model=VAR(train_diff)

        # Run VAR with different order (1-20)
        results_aic =[]
        for p in range(1,21):
            results = var_model.fit(p)
            results_aic.append(results.aic)

        # Store optimal p order
        optimal_p = list(np.arange(1,21,1))[np.argmin(results_aic)]

        # Refit var with optimal p
        best_var = var_model.fit(optimal_p)

        # Make 1-step ahead forecast
        yhat_var = best_var.forecast(var_model.endog, steps=1)

        # clean up yhat
        df_yhat_var = pd.DataFrame(yhat_var)
        df_yhat_var.index = [test_diff.index[i]]
        df_yhat_var.columns = test_diff.columns
 

        # Store df_yhat_var
        df_pred = df_pred.append(df_yhat_var)

        # Add actual 1-steap ahead actual test data into training set and drop 1st observation from training data
        train_diff = train_diff.append(test_diff.copy().iloc[i])[1:]
       
        # Print progress
        if verbose:
            print(f"Index {i + 1}")
            print("Optimal p with minimum AIC: ", optimal_p)
            print("One-step ahead forecast (differened data)")
            display(df_yhat_var)
    
    # Recover first order differencing
    df_pred_var = pd.concat([train.tail(1), df_pred], axis=0).cumsum()
    df_pred_var = df_pred_var[-23:]

    # Extract predictions for eneos
    y_pred_var = df_pred_var["eneos"]

    # Return prediction
    return y_pred_var


pred_rolling_var_all = rolling_var(exog_list=['jp_gdp', 'jp_unemp', 'oil', 'usdjpy', 'jp_i', 'n225'], verbose=True)

Index 1
Optimal p with minimum AIC:  3
One-step ahead forecast (differened data)

Index 2
Optimal p with minimum AIC:  3
One-step ahead forecast (differened data)

Index 3
Optimal p with minimum AIC:  3
One-step ahead forecast (differened data)

Index 4
Optimal p with minimum AIC:  3
One-step ahead forecast (differened data)

Index 5
Optimal p with minimum AIC:  4
One-step ahead forecast (differened data)

Index 6
Optimal p with minimum AIC:  3
One-step ahead forecast (differened data)

Index 7
Optimal p with minimum AIC:  3
One-step ahead forecast (differened data)

Index 8
Optimal p with minimum AIC:  3
One-step ahead forecast (differened data)

Index 9
Optimal p with minimum AIC:  3
One-step ahead forecast (differened data)

Index 10
Optimal p with minimum AIC:  3
One-step ahead forecast (differened data)


print("Rolling Var / all exog")
make_plot(y_train, y_test, pred_rolling_var_all, "Rolling Var / all exog")
metrics_rolling_var_all = calc_metrics(y_test, pred_rolling_var_all, return_dict=True)

Rolling Var / all exog

Test Error Metrics
MAE: 14.9596
MSE: 422.0461
MAPE: 0.0339
sMAPE: 0.0328
MASE: 19.834


pred_rolling_var_n225 = rolling_var(exog_list=['n225'])


print("Rolling Var / n225")
make_plot(y_train, y_test, pred_rolling_var_n225, "Rolling Var / n225")
metrics_rolling_var_n225 = calc_metrics(y_test, pred_rolling_var_n225, return_dict=True)

Rolling Var / n225

Test Error Metrics
MAE: 9.6287
MSE: 170.5378
MAPE: 0.0218
sMAPE: 0.0214
MASE: 12.766


pred_rolling_var_oilusdjpy = rolling_var(exog_list=['oil', 'usdjpy'])


print("Rolling Var / oil & usdjpy")
make_plot(y_train, y_test, pred_rolling_var_oilusdjpy, "Rolling Var / oil & usdjpy")
metrics_rolling_var_oilusdjpy = calc_metrics(y_test, pred_rolling_var_oilusdjpy, return_dict=True)

Rolling Var / oil & usdjpy

Test Error Metrics
MAE: 12.0597
MSE: 294.9881
MAPE: 0.0274
sMAPE: 0.0267
MASE: 15.9891


pred_rolling_var_gdpunemp = rolling_var(exog_list=['jp_gdp', 'jp_unemp'])


print("Rolling Var / GDP & Unemp")
make_plot(y_train, y_test, pred_rolling_var_gdpunemp, "Rolling Var / GDP & Unemp")
metrics_rolling_var_gdpunemp = calc_metrics(y_test, pred_rolling_var_gdpunemp, return_dict=True)

Rolling Var / GDP & Unemp

Test Error Metrics
MAE: 9.5726
MSE: 175.8181
MAPE: 0.0217
sMAPE: 0.0213
MASE: 12.6917


# Library
from statsmodels.tsa.vector_ar.var_model import VAR

# Function to run VAR
def rolling_var2(exog_list, train_diff_raw=df_train_diff, test_diff_raw=df_test_diff, train_raw=df_train, verbose=False):
    """
    ***** Use only last 52 observations as training instead of whole training data *****
    Input:
        (1) exog_list: column names for external regressors
        (2) train_diff_raw: df_train_diff (differenced training data)
        (3) test_diff_raw: df for extracting index / exog for training
        (4) train_raw: df_train (non-differenced training data)
    Process:
        (1) Build model using VAR() with optimal order p in terms of AIC using whole differenced training data
        (2) Make one-step ahead prediction & Store predicted values
        (3) Add 1-step ahead true values into differenced training data and drop first observation from it
        (5) Repeat (1) through (3) over test data periods
    Outoput:
        - Prediction for Eneos (23-step ahead)
    """
    # Slice data by eneos and specified exog
    train_diff = train_diff_raw[["eneos"] + exog_list][-52:]
    test_diff = test_diff_raw[["eneos"] + exog_list]
    train = train_raw[["eneos"] + exog_list][-52:]

    # DF to store predicted values
    df_pred = pd.DataFrame(columns=train.columns)

    # Fit var model and make 1-step ahead prediction
    for i in range(test_diff.shape[0]):

        # Create instance
        var_model=VAR(train_diff)

        # Run VAR with different order (1-20)
        results_aic =[]
        for p in range(1,6):
            results = var_model.fit(p)
            results_aic.append(results.aic)

        # Store optimal p order
        optimal_p = list(np.arange(1,6,1))[np.argmin(results_aic)]

        # Refit var with optimal p
        best_var = var_model.fit(optimal_p)

        # Make 1-step ahead forecast
        yhat_var = best_var.forecast(var_model.endog, steps=1)

        # clean up yhat
        df_yhat_var = pd.DataFrame(yhat_var)
        df_yhat_var.index = [test_diff.index[i]]
        df_yhat_var.columns = test_diff.columns
 

        # Store df_yhat_var
        df_pred = df_pred.append(df_yhat_var)

        # Add actual 1-steap ahead actual test data into training set and drop 1st observation from training data
        train_diff = train_diff.append(test_diff.copy().iloc[i])[1:]
       
        # Print progress
        if verbose:
            print(f"Index {i + 1}")
            print("Optimal p with minimum AIC: ", optimal_p)
            print("One-step ahead forecast (differened data)")
            display(df_yhat_var)
    
    # Recover first order differencing
    df_pred_var = pd.concat([train.tail(1), df_pred], axis=0).cumsum()
    df_pred_var = df_pred_var[-23:]

    # Extract predictions for eneos
    y_pred_var = df_pred_var["eneos"]

    # Return prediction
    return y_pred_var


pred_rolling_var_all2 = rolling_var2(exog_list=['jp_gdp', 'jp_unemp', 'oil', 'usdjpy', 'jp_i', 'n225'], verbose=True)

Index 1
Optimal p with minimum AIC:  5
One-step ahead forecast (differened data)

Index 2
Optimal p with minimum AIC:  5
One-step ahead forecast (differened data)

Index 3
Optimal p with minimum AIC:  5
One-step ahead forecast (differened data)

Index 4
Optimal p with minimum AIC:  5
One-step ahead forecast (differened data)

Index 5
Optimal p with minimum AIC:  5
One-step ahead forecast (differened data)

Index 6
Optimal p with minimum AIC:  5
One-step ahead forecast (differened data)

Index 7
Optimal p with minimum AIC:  5
One-step ahead forecast (differened data)

Index 8
Optimal p with minimum AIC:  5
One-step ahead forecast (differened data)

Index 9
Optimal p with minimum AIC:  5
One-step ahead forecast (differened data)

Index 10
Optimal p with minimum AIC:  5
One-step ahead forecast (differened data)


print("Rolling Var2 / all exog")
make_plot(y_train, y_test, pred_rolling_var_all2, "Rolling Var2 / all exog")
metrics_rolling_var_all2 = calc_metrics(y_test, pred_rolling_var_all2, return_dict=True)

Rolling Var2 / all exog

Test Error Metrics
MAE: 50.3905
MSE: 3522.3065
MAPE: 0.1121
sMAPE: 0.1041
MASE: 66.8095


pred_rolling_var_n2252 = rolling_var2(exog_list=['n225'])


print("Rolling Var2 / n225")
make_plot(y_train, y_test, pred_rolling_var_n2252, "Rolling Var2 / n225")
metrics_rolling_var_n2252 = calc_metrics(y_test, pred_rolling_var_n2252, return_dict=True)

Rolling Var2 / n225

Test Error Metrics
MAE: 18.0353
MSE: 531.7428
MAPE: 0.0408
sMAPE: 0.0394
MASE: 23.9118


pred_rolling_var_oilusdjpy2 = rolling_var2(exog_list=['oil', 'usdjpy'])


print("Rolling Var2 / oil & usdjpy")
make_plot(y_train, y_test, pred_rolling_var_oilusdjpy2, "Rolling Var2 / oil & usdjpy")
metrics_rolling_var_oilusdjpy2 = calc_metrics(y_test, pred_rolling_var_oilusdjpy2, return_dict=True)

Rolling Var2 / oil & usdjpy

Test Error Metrics
MAE: 14.6472
MSE: 353.8647
MAPE: 0.0331
sMAPE: 0.0322
MASE: 19.4197


pred_rolling_var_gdpunemp2 = rolling_var2(exog_list=['jp_gdp', 'jp_unemp'])


print("Rolling Var2 / GDP & Unemp")
make_plot(y_train, y_test, pred_rolling_var_gdpunemp2, "Rolling Var2 / GDP & Unemp")
metrics_rolling_var_gdpunemp2 = calc_metrics(y_test, pred_rolling_var_gdpunemp2, return_dict=True)

Rolling Var2 / GDP & Unemp

Test Error Metrics
MAE: 28.0494
MSE: 1056.3627
MAPE: 0.0629
sMAPE: 0.0603
MASE: 37.1889


# Store all predictions and metrics
weekly_rolling_pred = dict()
weekly_rolling_metrics = dict()

# Rolling Univariate ARIMA(4)
weekly_rolling_pred["Rolling ARIMA / No-exog"] = pred_airma_rolling_uni4
weekly_rolling_metrics["Rolling ARIMA / No-exog"] = metrics_airma_rolling_uni4

# Rolling ARIMAX with external regressors (4)
weekly_rolling_pred["Rolling ARIMAX / All"] = pred_rolling_arimax_all4
weekly_rolling_metrics["Rolling ARIMAX / All"] = metrics_rolling_arimax_all4

weekly_rolling_pred["Rolling ARIMAX / Nikkei225"] = pred_rolling_arimax_n2254
weekly_rolling_metrics["Rolling ARIMAX / Nikkei225"] = metrics_rolling_arimax_n2254

weekly_rolling_pred["Rolling ARIMAX / Oil & USDJPY"] = pred_rolling_arimax_oilusdjpy4
weekly_rolling_metrics["Rolling ARIMAX / Oil & USDJPY"] = metrics_rolling_arimax_oilusdjpy4

weekly_rolling_pred["Rolling ARIMAX / GDP & Unemp"] = pred_rolling_arimax_gdpunemp4
weekly_rolling_metrics["Rolling ARIMAX / GDP & Unemp"] = metrics_rolling_arimax_gdpunemp4

# Rolling VAR
weekly_rolling_pred["Rolling VAR / All"] = pred_rolling_var_all
weekly_rolling_metrics["Rolling VAR / All"] = metrics_rolling_var_all

weekly_rolling_pred["Rolling VAR / Nikkei225"] = pred_rolling_var_n225
weekly_rolling_metrics["Rolling VAR / Nikkei225"] = metrics_rolling_var_n225

weekly_rolling_pred["Rolling VAR / Oil & USDJPY"] = pred_rolling_var_oilusdjpy
weekly_rolling_metrics["Rolling VAR / Oil & USDJPY"] = metrics_rolling_var_oilusdjpy

weekly_rolling_pred["Rolling VAR / GDP & Unemp"] = pred_rolling_var_gdpunemp
weekly_rolling_metrics["Rolling VAR / GDP & Unemp"] = metrics_rolling_var_gdpunemp


pd.DataFrame(weekly_rolling_metrics).T


pd.DataFrame(weekly_rolling_metrics).T.sort_values("sMAPE")


fig, ax = plt.subplots(figsize=(16,5))
y_train[-20:].plot(ax=ax, label="Training")
y_test.plot(ax=ax, label="Test", color="black")
for model in weekly_rolling_pred.keys():
    weekly_rolling_pred[model].plot(ax=ax, label=model, linestyle="dashed")
plt.legend()
plt.grid()
plt.show()

	type	count	NAs	(%)	unique	min	max	mean
RowId	object	2332531	0	-	2332531	-	-	-
Date	object	2332531	0	-	1202	-	-	-
SecuritiesCode	int64	2332531	0	-	2000	1301.0	9997.0	5894.835185
Open	float64	2324923	7608	0.3	23067	14.0	109950.0	2594.510783
High	float64	2324923	7608	0.3	23960	15.0	110500.0	2626.539682
Low	float64	2324923	7608	0.3	23904	13.0	107200.0	2561.227039
Close	float64	2324923	7608	0.3	24046	14.0	109550.0	2594.023446
Volume	int64	2332531	0	-	89006	0.0	643654000.0	691936.556556
AdjustmentFactor	float64	2332531	0	-	19	0.1	20.0	1.000508
ExpectedDividend	float64	18865	2313666	99.2	446	0.0	1070.0	22.01773
SupervisionFlag	bool	2332531	0	-	2	-	-	-
Target	float64	2332293	238	0.0	354507	-0.578541	1.119512	0.000445

	SecuritiesCode	EffectiveDate	Name	Section/Products	NewMarketSegment	33SectorCode	33SectorName	17SectorCode	17SectorName	NewIndexSeriesSizeCode	NewIndexSeriesSize	TradeDate	Close	IssuedShares	MarketCapitalization	Universe0	Category
4192	9514	20211230	EF-ON INC.	First Section (Domestic)	Prime Market	4050	Electric Power and Gas	11	ELECTRIC POWER & GAS	7	TOPIX Small 2	20211230.0	618.0	21636579.0	1.337141e+10	False	Other Electricity Service
4195	9522	20211230	Renewable Japan Co.,Ltd.	Mothers (Domestic)	Growth Market	4050	Electric Power and Gas	11	ELECTRIC POWER & GAS	-	-	20211230.0	1709.0	28420910.0	4.857134e+10	False	Other Electricity Service
2060	5002	20000101	VITEC HOLDINGS CO.,LTD.	First Section (Domestic)	NaN	3300	Oil and Coal Products	2	ENERGY RESOURCES	4	TOPIX Mid400	NaN	NaN	NaN	NaN	False	Other
2063	5010	20211230	NIPPON SEIRO CO.,LTD.	Second Section(Domestic)	Standard Market	3300	Oil and Coal Products	2	ENERGY RESOURCES	-	-	20211230.0	191.0	22400000.0	4.278400e+09	False	Oil Products Manufacturer
2065	5012	20000101	TonenGeneral Sekiyu K.K.	First Section (Domestic)	NaN	3300	Oil and Coal Products	2	ENERGY RESOURCES	4	TOPIX Mid400	NaN	NaN	NaN	NaN	False	Oil
2069	5018	20211230	MORESCO Corporation	First Section (Domestic)	Prime Market	3300	Oil and Coal Products	2	ENERGY RESOURCES	7	TOPIX Small 2	20211230.0	1161.0	9696500.0	1.125764e+10	False	Oil Products Manufacturer

	ADF	KPSS('c')	KPSS('ct')
Test Statistic	-1.201363	3.438455	0.722794
p-value	0.673009	0.010000	0.010000
Lags Used	9.000000	23.000000	23.000000
Critical Value (1%)	-3.435852	0.739000	0.216000
Critical Value (5%)	-2.863970	0.463000	0.146000
Critical Value (10%)	-2.568064	0.347000	0.119000

	ADF	KPSS('c')	KPSS('ct')
Test Statistic	-1.315887e+01	0.089789	0.0155
p-value	1.319894e-24	0.100000	0.1000
Lags Used	8.000000e+00	23.000000	23.0000
Critical Value (1%)	-3.435852e+00	0.739000	0.2160
Critical Value (5%)	-2.863970e+00	0.463000	0.1460
Critical Value (10%)	-2.568064e+00	0.347000	0.1190

	Tokyo Gas	oil	n225
Date
2017-01-04	2691.5	53.26	19594.160156
2017-01-05	2683.5	53.77	19520.689453
2017-01-06	2691.5	53.98	19454.330078
2017-01-10	2628.0	50.82	19301.439453
2017-01-11	2648.5	52.19	19364.669922
...	...	...	...
2021-11-29	1993.0	69.88	28283.919922
2021-11-30	1945.0	66.14	27821.759766
2021-12-01	1904.0	65.44	27935.619141
2021-12-02	1975.0	66.60	27753.369141
2021-12-03	1978.0	66.39	28029.570312

	type	count	NAs	(%)	unique	min	max	mean
SecuritiesCode	int64	4417	0	-	4417	1301.0	25935.0	5547.191306
EffectiveDate	int64	4417	0	-	10	20000101.0	20220225.0	20197579.726738
Name	object	4417	0	-	4411	-	-	-
Section/Products	object	4417	0	-	11	-	-	-
NewMarketSegment	object	3772	645	14.6	6	-	-	-
33SectorCode	object	4417	0	-	34	-	-	-
33SectorName	object	4417	0	-	34	-	-	-
17SectorCode	object	4417	0	-	18	-	-	-
17SectorName	object	4417	0	-	34	-	-	-
NewIndexSeriesSizeCode	object	4417	0	-	6	-	-	-
NewIndexSeriesSize	object	4417	0	-	6	-	-	-
TradeDate	float64	4121	296	6.7	10	20211216.0	20211230.0	20211229.954137
Close	float64	4121	296	6.7	2566	1.8	711000.0	6376.7347
IssuedShares	float64	4121	296	6.7	4011	2242.0	16314987460.0	89922667.041686
MarketCapitalization	float64	4121	296	6.7	4121	38786600.0	52192239810720.0	218440012227.214966
Universe0	bool	4417	0	-	2	-	-	-

	SecuritiesCode	EffectiveDate	Name	Section/Products	NewMarketSegment	33SectorCode	17SectorCode	17SectorName	NewIndexSeriesSizeCode	NewIndexSeriesSize	TradeDate	Close	IssuedShares	MarketCapitalization	Universe0
33SectorName
Information & Communication	551	551	551	551	538	551	551	551	551	551	539	539	539	539	551
Services	521	521	521	521	502	521	521	521	521	521	506	506	506	506	521
-	500	500	500	500	10	500	500	500	500	500	345	345	345	345	500
Retail Trade	359	359	359	359	337	359	359	359	359	359	339	339	339	339	359
Wholesale Trade	320	320	320	320	311	320	320	320	320	320	311	311	311	311	320
Electric Appliances	255	255	255	255	243	255	255	255	255	255	243	243	243	243	255
Machinery	230	230	230	230	227	230	230	230	230	230	228	228	228	228	230
Chemicals	218	218	218	218	214	218	218	218	218	218	214	214	214	214	218
Construction	170	170	170	170	157	170	170	170	170	170	157	157	157	157	170
Real Estate	143	143	143	143	137	143	143	143	143	143	137	137	137	137	143

	SecuritiesCode	Name	33SectorName	Category	Section/Products
4181	9501	Tokyo Electric Power Company Holdings,Incorpor...	Electric Power and Gas	Electric Utility	First Section (Domestic)
4182	9502	Chubu Electric Power Company,Incorporated	Electric Power and Gas	Electric Utility	First Section (Domestic)
4183	9503	The Kansai Electric Power Company,Incorporated	Electric Power and Gas	Electric Utility	First Section (Domestic)
4184	9504	The Chugoku Electric Power Company,Incorporated	Electric Power and Gas	Electric Utility	First Section (Domestic)
4185	9505	Hokuriku Electric Power Company	Electric Power and Gas	Electric Utility	First Section (Domestic)
4186	9506	Tohoku Electric Power Company,Incorporated	Electric Power and Gas	Electric Utility	First Section (Domestic)
4187	9507	Shikoku Electric Power Company,Incorporated	Electric Power and Gas	Electric Utility	First Section (Domestic)
4188	9508	Kyushu Electric Power Company,Incorporated	Electric Power and Gas	Electric Utility	First Section (Domestic)
4189	9509	Hokkaido Electric Power Company,Incorporated	Electric Power and Gas	Electric Utility	First Section (Domestic)
4190	9511	The Okinawa Electric Power Company,Incorporated	Electric Power and Gas	Electric Utility	First Section (Domestic)
4191	9513	Electric Power Development Co.,Ltd.	Electric Power and Gas	Electric Utility	First Section (Domestic)
4192	9514	EF-ON INC.	Electric Power and Gas	Other Electricity Service	First Section (Domestic)
4193	9517	eREX Co.,Ltd.	Electric Power and Gas	Other Electricity Service	First Section (Domestic)
4194	9519	RENOVA,Inc.	Electric Power and Gas	Other Electricity Service	First Section (Domestic)
4195	9522	Renewable Japan Co.,Ltd.	Electric Power and Gas	Other Electricity Service	Mothers (Domestic)
4196	9531	TOKYO GAS CO.,LTD.	Electric Power and Gas	Gas Utility	First Section (Domestic)
4197	9532	OSAKA GAS CO.,LTD.	Electric Power and Gas	Gas Utility	First Section (Domestic)
4198	9533	TOHO GAS CO.,LTD.	Electric Power and Gas	Gas Utility	First Section (Domestic)
4199	9534	HOKKAIDO GAS CO.,LTD.	Electric Power and Gas	Gas Utility	First Section (Domestic)
4200	9535	HIROSHIMA GAS CO.,LTD.	Electric Power and Gas	Gas Utility	First Section (Domestic)
4201	9536	SAIBU GAS HOLDINGS CO.,LTD.	Electric Power and Gas	Gas Utility	First Section (Domestic)
4202	9537	HOKURIKU GAS CO.,LTD.	Electric Power and Gas	Gas Utility	Second Section(Domestic)
4203	9539	KEIYO GAS CO.,LTD.	Electric Power and Gas	Gas Utility	Second Section(Domestic)
4204	9543	SHIZUOKA GAS CO.,LTD.	Electric Power and Gas	Gas Utility	First Section (Domestic)
4205	9551	METAWATER Co.,Ltd.	Electric Power and Gas	Other	First Section (Domestic)
1044	3315	NIPPON COKE & ENGINEERING COMPANY,LIMITED	Oil and Coal Products	Oil Products Manufacturer	First Section (Domestic)
2060	5002	VITEC HOLDINGS CO.,LTD.	Oil and Coal Products	Other	First Section (Domestic)
2061	5008	TOA OIL COMPANY,LIMITED	Oil and Coal Products	Oil	Second Section(Domestic)
2063	5010	NIPPON SEIRO CO.,LTD.	Oil and Coal Products	Oil Products Manufacturer	Second Section(Domestic)
2064	5011	NICHIREKI CO.,LTD.	Oil and Coal Products	Oil Products Manufacturer	First Section (Domestic)
2065	5012	TonenGeneral Sekiyu K.K.	Oil and Coal Products	Oil	First Section (Domestic)
2066	5013	Yushiro Chemical Industry Co.,Ltd.	Oil and Coal Products	Oil Products Manufacturer	First Section (Domestic)
2067	5015	BP Castrol K.K.	Oil and Coal Products	Oil Products Manufacturer	First Section (Domestic)
2068	5017	Fuji Oil Company,Ltd.	Oil and Coal Products	Oil	First Section (Domestic)
2069	5018	MORESCO Corporation	Oil and Coal Products	Oil Products Manufacturer	First Section (Domestic)
2070	5019	Idemitsu Kosan Co.,Ltd.	Oil and Coal Products	Oil	First Section (Domestic)
2071	5020	ENEOS Holdings,Inc.	Oil and Coal Products	Oil	First Section (Domestic)
2072	5021	COSMO ENERGY HOLDINGS COMPANY,LIMITED	Oil and Coal Products	Oil	First Section (Domestic)

	Date	SecuritiesCode	Close	Name	Category
Date
2017-09-21	2017-09-21	9531	564.7	Tokyo Gas	Gas Utility
2017-09-22	2017-09-22	9531	567.7	Tokyo Gas	Gas Utility
2017-09-25	2017-09-25	9531	560.1	Tokyo Gas	Gas Utility
2017-09-26	2017-09-26	9531	564.4	Tokyo Gas	Gas Utility
2017-09-27	2017-09-27	9531	2763.0	Tokyo Gas	Gas Utility
2017-09-28	2017-09-28	9531	2844.0	Tokyo Gas	Gas Utility
2017-09-29	2017-09-29	9531	2758.0	Tokyo Gas	Gas Utility
2017-09-21	2017-09-21	9532	420.4	Osaka Gas	Gas Utility
2017-09-22	2017-09-22	9532	422.1	Osaka Gas	Gas Utility
2017-09-25	2017-09-25	9532	425.2	Osaka Gas	Gas Utility
2017-09-26	2017-09-26	9532	429.8	Osaka Gas	Gas Utility
2017-09-27	2017-09-27	9532	2094.5	Osaka Gas	Gas Utility
2017-09-28	2017-09-28	9532	2123.0	Osaka Gas	Gas Utility
2017-09-29	2017-09-29	9532	2092.0	Osaka Gas	Gas Utility

	ADF	KPSS('c')	KPSS('ct')
Test Statistic	-0.666585	1.195419	0.302181
p-value	0.855216	0.010000	0.010000
Lags Used	4.000000	16.000000	16.000000
Critical Value (1%)	-3.456569	0.739000	0.216000
Critical Value (5%)	-2.873079	0.463000	0.146000
Critical Value (10%)	-2.572919	0.347000	0.119000

	ADF	KPSS('c')	KPSS('ct')
Test Statistic	-9.766553e+00	0.161865	0.026794
p-value	7.323609e-17	0.100000	0.100000
Lags Used	3.000000e+00	16.000000	16.000000
Critical Value (1%)	-3.456569e+00	0.739000	0.216000
Critical Value (5%)	-2.873079e+00	0.463000	0.146000
Critical Value (10%)	-2.572919e+00	0.347000	0.119000

	Tokyo Gas	jp_gdp	jp_unemp	oil	usdjpy	jp_i	n225
Date
2017-01-01	NaN	547306.2	3.1	NaN	NaN	NaN	NaN
2021-10-10	2050.30	NaN	2.8	78.504000	111.295401	0.07200	27904.605859
2021-10-17	1939.30	NaN	2.8	81.176000	113.262399	0.08740	28497.729687
2021-10-24	1907.70	NaN	2.8	83.476000	114.278200	0.09280	29001.992188
2021-10-31	1910.00	NaN	2.8	83.844000	113.801801	0.09940	28903.487891
2021-11-07	2021.75	NaN	2.9	81.788000	114.039799	0.08300	29643.479980
2021-11-14	1990.20	NaN	2.9	81.930000	113.517799	0.06840	29357.424219
2021-11-21	1949.20	NaN	2.9	78.992000	114.297801	0.08020	29723.555859
2021-11-28	1997.75	NaN	2.9	77.793333	114.909200	0.08475	29331.916992
2021-12-05	1959.00	NaN	2.8	66.890000	113.345203	0.06980	27964.847656
2021-12-12	NaN	NaN	NaN	71.314000	113.431400	0.05800	28481.365625
2021-12-19	NaN	NaN	NaN	71.184000	113.724001	0.05820	28628.970313
2021-12-26	NaN	NaN	NaN	71.625000	113.950601	0.06920	28519.714062
2022-01-02	NaN	NaN	NaN	76.048000	114.781801	0.07950	28861.053223

	MAE	MSE	MAPE	sMAPE	MASE
ARIMA(0,1,1) / No-	131.9129	28228.7658	0.0661	0.0627	-1.1125
ARIMAX(0,1,1) / all	77.2154	10671.9102	0.0388	0.0375	-0.6512
ARIMAX(0,1,1) / n225	78.5779	10447.2298	0.0393	0.0382	-0.6627
ARIMAX(0,1,1) / oil	129.9804	27404.4503	0.0652	0.0618	-1.0962

	tokyo	oil
Date
2021-01-04	-4.650032	-0.247341
2021-01-05	-10.324048	-0.155952
2021-01-06	2.018371	0.042515
2021-01-07	1.968440	-0.135240
2021-01-08	0.930132	0.061009
...	...	...
2021-11-29	-0.298810	-0.004684
2021-11-30	-0.298810	-0.004684
2021-12-01	-0.298810	-0.004684
2021-12-02	-0.298810	-0.004684
2021-12-03	-0.298810	-0.004684

	tokyo	oil	n225
Date
2021-01-04	11.688611	0.853693	99.427897
2021-01-05	2.689187	-0.254569	28.897992
2021-01-06	1.638704	-1.446170	19.718546
2021-01-07	-12.107077	1.342011	-37.381688
2021-01-08	-0.264490	1.536821	-17.597606
...	...	...	...
2021-11-29	-0.158020	-0.004643	8.979042
2021-11-30	-0.158013	-0.004643	8.979046
2021-12-01	-0.158008	-0.004643	8.979024
2021-12-02	-0.158005	-0.004644	8.978982
2021-12-03	-0.158006	-0.004644	8.978933

	tokyo	oil	n225	jp_unemp
Date
2021-01-04	0.188015	0.419958	61.437427	-0.002616
2021-01-05	-1.670987	-0.351860	1.642294	0.000852
2021-01-06	-0.350625	0.098725	13.832494	-0.000179
2021-01-07	-0.091842	0.001737	5.826075	0.000130
2021-01-08	-0.354250	-0.019515	9.837397	0.000086
...	...	...	...	...
2021-11-29	-0.316197	-0.005540	8.283459	0.000100
2021-11-30	-0.316197	-0.005540	8.283459	0.000100
2021-12-01	-0.316197	-0.005540	8.283459	0.000100
2021-12-02	-0.316197	-0.005540	8.283459	0.000100
2021-12-03	-0.316197	-0.005540	8.283459	0.000100

	tokyo	oil	n225	jp_unemp	jp_gdp
Date
2021-01-04	6.479636	0.102098	86.754079	0.002943	-506.777595
2021-01-05	-1.216366	0.075738	-12.227668	0.005096	-21.508014
2021-01-06	3.386518	-0.012620	43.704692	-0.005312	-140.902446
2021-01-07	-9.955103	0.331145	-24.920802	-0.001603	-868.136344
2021-01-08	2.861119	0.558415	13.154791	-0.000842	-847.139945
...	...	...	...	...	...
2021-11-29	-0.300903	-0.001475	8.935765	0.000080	-1.497658
2021-11-30	-0.300903	-0.001475	8.935766	0.000080	-1.497658
2021-12-01	-0.300903	-0.001475	8.935766	0.000080	-1.497661
2021-12-02	-0.300903	-0.001475	8.935766	0.000080	-1.497661
2021-12-03	-0.300903	-0.001475	8.935765	0.000080	-1.497659

	tokyo	oil	n225	jp_unemp	jp_gdp	usdjpy
Date
2021-01-04	2.372628	0.287518	73.167477	0.002115	-482.781396	-0.175379
2021-01-05	0.345862	0.294738	11.520023	0.004589	-31.465788	-0.128185
2021-01-06	5.309567	0.067789	25.945321	-0.005274	22.596011	0.019328
2021-01-07	-5.928458	0.196840	-2.026457	0.000696	-961.812042	-0.116844
2021-01-08	3.009113	0.635541	18.285359	-0.000467	-802.567411	0.106791
...	...	...	...	...	...	...
2021-11-29	-0.285417	-0.002314	8.825160	0.000091	-2.882649	-0.010832
2021-11-30	-0.285417	-0.002314	8.825163	0.000091	-2.882663	-0.010832
2021-12-01	-0.285417	-0.002314	8.825166	0.000091	-2.882650	-0.010832
2021-12-02	-0.285417	-0.002314	8.825165	0.000091	-2.882632	-0.010832
2021-12-03	-0.285417	-0.002314	8.825165	0.000091	-2.882650	-0.010832

	tokyo	jp_gdp	jp_unemp	oil	usdjpy	jp_i	n225
Date
2021-01-04	9.709107	-113.410223	-0.001618	0.179858	-0.139402	-0.001512	78.150147
2021-01-05	8.741641	75.065053	0.003261	0.089964	-0.054060	-0.000822	38.893853
2021-01-06	2.219266	-77.555580	-0.008300	0.148149	-0.066364	0.002384	33.240096
2021-01-07	-10.834405	-624.137319	0.000243	0.408428	0.000294	0.000256	-38.528112
2021-01-08	2.062588	-1095.489061	0.002165	0.280710	0.106668	0.002013	27.572715
...	...	...	...	...	...	...	...
2021-11-29	-0.282191	-0.951496	0.000110	-0.003702	-0.011049	-0.000055	8.415911
2021-11-30	-0.282192	-0.951481	0.000110	-0.003702	-0.011049	-0.000055	8.415910
2021-12-01	-0.282191	-0.951473	0.000110	-0.003702	-0.011049	-0.000055	8.415906
2021-12-02	-0.282191	-0.951510	0.000110	-0.003702	-0.011049	-0.000055	8.415908
2021-12-03	-0.282191	-0.951512	0.000110	-0.003702	-0.011049	-0.000055	8.415908

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	additive_terms	additive_terms_lower	additive_terms_upper	weekly	weekly_lower	weekly_upper	yearly	yearly_lower	yearly_upper	yhat
0	2017-01-04	2618.951503	2490.847581	2697.074230	2618.951503	2618.951503	-22.638445	-22.638445	-22.638445	-7.441870	-7.441870	-7.441870	-15.196575	-15.196575	-15.196575	2596.313057
1	2017-01-05	2619.616665	2499.469519	2699.442227	2619.616665	2619.616665	-23.379497	-23.379497	-23.379497	-11.277116	-11.277116	-11.277116	-12.102380	-12.102380	-12.102380	2596.237168
2	2017-01-06	2620.281827	2502.258062	2698.550801	2620.281827	2620.281827	-22.732299	-22.732299	-22.732299	-13.295097	-13.295097	-13.295097	-9.437203	-9.437203	-9.437203	2597.549527

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	additive_terms	additive_terms_lower	additive_terms_upper	extra_regressors_additive	...	weekly	weekly_lower	weekly_upper	yearly	yearly_lower	yearly_upper	yhat
0	2017-01-04	2753.634345	2543.559076	2728.107631	2753.634345	2753.634345	-116.943238	-116.943238	-116.943238	-94.172335	...	19.848219	19.848219	19.848219	-42.619122	-42.619122	-42.619122	2636.691108
1	2017-01-05	2753.309951	2534.905638	2730.342785	2753.309951	2753.309951	-123.723115	-123.723115	-123.723115	-100.173035	...	16.739797	16.739797	16.739797	-40.289877	-40.289877	-40.289877	2629.586835
2	2017-01-06	2752.985556	2526.241706	2718.228527	2752.985556	2752.985556	-127.609524	-127.609524	-127.609524	-104.221791	...	15.027839	15.027839	15.027839	-38.415572	-38.415572	-38.415572	2625.376032

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	additive_terms	additive_terms_lower	additive_terms_upper	yearly	yearly_lower	yearly_upper	yhat
0	2017-01-08	2679.856082	2520.912654	2816.145145	2679.856082	2679.856082	-10.684018	-10.684018	-10.684018	-10.684018	-10.684018	-10.684018	2669.172064
1	2017-01-15	2682.312208	2536.257599	2831.972440	2682.312208	2682.312208	-0.999257	-0.999257	-0.999257	-0.999257	-0.999257	-0.999257	2681.312951
2	2017-01-22	2684.768334	2537.962647	2813.673938	2684.768334	2684.768334	-18.771677	-18.771677	-18.771677	-18.771677	-18.771677	-18.771677	2665.996658

	ADF	KPSS('c')	KPSS('ct')
Test Statistic	-1.541135	3.73534	0.701049
p-value	0.513073	0.01000	0.010000
Lags Used	8.000000	20.00000	20.000000
Critical Value (1%)	-3.435848	0.73900	0.216000
Critical Value (5%)	-2.863968	0.46300	0.146000
Critical Value (10%)	-2.568063	0.34700	0.119000

	ADF	KPSS('c')	KPSS('ct')
Test Statistic	-1.402885	1.17686	0.264062
p-value	0.580892	0.01000	0.010000
Lags Used	1.000000	10.00000	10.000000
Critical Value (1%)	-3.456257	0.73900	0.216000
Critical Value (5%)	-2.872942	0.46300	0.146000
Critical Value (10%)	-2.572846	0.34700	0.119000

	ADF	KPSS('c')	KPSS('ct')
Test Statistic	-1.243787e+01	0.138115	0.098419
p-value	3.811269e-23	0.100000	0.100000
Lags Used	0.000000e+00	3.000000	3.000000
Critical Value (1%)	-3.456257e+00	0.739000	0.216000
Critical Value (5%)	-2.872942e+00	0.463000	0.146000
Critical Value (10%)	-2.572846e+00	0.347000	0.119000

	eneos	jp_gdp	jp_unemp	oil	usdjpy	jp_i	n225
Date
2021-10-10	454.200	NaN	2.8	78.504000	111.295401	0.07200	27904.605859
2021-10-17	460.300	NaN	2.8	81.176000	113.262399	0.08740	28497.729687
2021-10-24	467.280	NaN	2.8	83.476000	114.278200	0.09280	29001.992188
2021-10-31	464.500	NaN	2.8	83.844000	113.801801	0.09940	28903.487891
2021-11-07	462.025	NaN	2.9	81.788000	114.039799	0.08300	29643.479980
2021-11-14	459.300	NaN	2.9	81.930000	113.517799	0.06840	29357.424219
2021-11-21	443.880	NaN	2.9	78.992000	114.297801	0.08020	29723.555859
2021-11-28	436.075	NaN	2.9	77.793333	114.909200	0.08475	29331.916992
2021-12-05	425.140	NaN	2.8	66.890000	113.345203	0.06980	27964.847656

	eneos	jp_gdp	jp_unemp	oil	usdjpy	jp_i	n225
Date
2017-01-08	510.933333	547306.2	3.1	53.3425	116.865399	0.058333	19523.059896
2017-01-15	514.000000	547306.2	3.1	52.0660	115.753801	0.052250	19272.021973
2017-01-22	515.660000	547306.2	3.1	51.8225	114.199800	0.059200	19002.659766
2017-01-29	526.200000	547306.2	3.1	52.7420	113.635599	0.068200	19121.262109
2017-02-05	531.400000	547306.2	3.1	53.3280	113.432199	0.096200	19078.209766
...	...	...	...	...	...	...	...
2021-05-30	453.560000	544693.4	3.1	66.3980	109.110199	0.081200	28651.839844
2021-06-06	462.780000	544693.4	3.1	68.7425	109.750798	0.087000	28924.037891
2021-06-13	470.080000	544693.4	3.1	70.1120	109.475800	0.067000	28950.178516
2021-06-20	470.500000	544693.4	3.1	71.5460	110.185799	0.058600	29175.304297
2021-06-27	466.940000	544693.4	3.1	73.4840	110.632399	0.060400	28742.272266

	eneos	jp_gdp	jp_unemp	oil	usdjpy	jp_i	n225
Date
2021-07-04	468.480000	538923.3	2.9	74.068000	110.931200	0.060800	28828.495312
2021-07-11	468.260000	538923.3	2.9	73.345000	110.617801	0.033000	28333.359766
2021-07-18	472.900000	538923.3	2.9	73.188000	110.179399	0.020600	28435.583984
2021-07-25	453.900000	538923.3	2.9	69.684000	109.944598	0.015667	27529.633464
2021-08-01	460.400000	538923.3	2.9	72.750000	109.990399	0.019000	27690.235938
2021-08-08	464.960000	538923.3	2.9	69.500000	109.449399	0.014000	27711.017578
2021-08-15	466.850000	538923.3	2.9	68.334000	110.388000	0.032250	27987.707520
2021-08-22	431.860000	538923.3	2.9	65.048000	109.613600	0.015800	27365.598047
2021-08-29	421.980000	538923.3	2.9	67.590000	109.854399	0.025800	27666.914062
2021-09-05	430.480000	538923.3	2.9	69.150000	109.981200	0.035200	28400.293359
2021-09-12	446.980000	538923.3	2.9	68.982500	109.975800	0.049600	30029.454297
2021-09-19	460.880000	538923.3	2.9	71.688000	109.742001	0.050400	30490.514062
2021-09-26	460.166667	538923.3	2.9	72.180000	109.740999	0.051333	29909.307292
2021-10-03	462.480000	540745.2	2.8	75.454000	111.330598	0.074400	29638.408203
2021-10-10	454.200000	540745.2	2.8	78.504000	111.295401	0.072000	27904.605859
2021-10-17	460.300000	540745.2	2.8	81.176000	113.262399	0.087400	28497.729687
2021-10-24	467.280000	540745.2	2.8	83.476000	114.278200	0.092800	29001.992188
2021-10-31	464.500000	540745.2	2.8	83.844000	113.801801	0.099400	28903.487891
2021-11-07	462.025000	540745.2	2.9	81.788000	114.039799	0.083000	29643.479980
2021-11-14	459.300000	540745.2	2.9	81.930000	113.517799	0.068400	29357.424219
2021-11-21	443.880000	540745.2	2.9	78.992000	114.297801	0.080200	29723.555859
2021-11-28	436.075000	540745.2	2.9	77.793333	114.909200	0.084750	29331.916992
2021-12-05	425.140000	540745.2	2.8	66.890000	113.345203	0.069800	27964.847656

	MAE	MSE	MAPE	sMAPE	MASE
Rolling ARIMA / No-exog	8.2791	127.8672	0.0185	0.0184	10.9768
Rolling ARIMAX / All	7.7303	131.0375	0.0174	0.0171	10.2491
Rolling ARIMAX / Nikkei225	7.4110	127.3857	0.0166	0.0164	9.8258
Rolling ARIMAX / Oil & USDJPY	8.2142	127.4794	0.0185	0.0182	10.8906
Rolling ARIMAX / GDP & Unemp	8.0840	123.1674	0.0181	0.0179	10.7180
Rolling VAR / All	14.9596	422.0461	0.0339	0.0328	19.8340
Rolling VAR / Nikkei225	9.6287	170.5378	0.0218	0.0214	12.7660
Rolling VAR / Oil & USDJPY	12.0597	294.9881	0.0274	0.0267	15.9891
Rolling VAR / GDP & Unemp	9.5726	175.8181	0.0217	0.0213	12.6917

JPX Tokyo Stock Exchange Prediction: Tokyo Gas Study Case¶

Preliminaries¶

Functions¶

Stock Data Load¶

External Data Load¶

EDA¶

Industry EDA¶

Energy Comapny list¶

Merge data¶

Plots by category¶

Elextric Industry¶

Gas Industry¶

Oil Industry¶

Other energy related companies¶

Main 5 Companies¶

ARIMA Models(Tokyo Gas)¶

Daily Analysis ARIMA(1 Year Prediction)¶

Univariate ARIMA¶

Multivariate ARIMAX¶

With Oil Regressor¶

With NIKKEI225 Regressor¶

Oil & Nikkei¶

Weekly Analysis ARIMA (6 Monthes Prediction)¶

Pre-processing & stationarity check for weekly data¶

Pre-processing for external regressors¶

Data Splitting¶

ARIMA Model Pipeline and Visualization¶

Univariate ARIMA¶

Multivariate ARIMAX¶

NIKKEI 225 Regressor¶

Oil Regressor¶

All external regressors¶

VAR Model (Tokyo Gas)¶

Pre-processing & stationarity check¶

Vector Auto Regression (VAR) - Oil¶

Vector Auto Regression (VAR) - Oil & N225¶

Vector Auto Regression (VAR) - Oil, N225, Unemployment¶

Vector Auto Regression (VAR) - Oil, N225, Unemployement, GDP¶

Vector Auto Regression (VAR) - Oil, N225, Unemployement, GDP, USD-JPY rate¶

Vector Auto Regression (VAR) - All External Data¶

Prophet (Tokyo Gas)¶

Daily Analysis Prophet (1 Year Prediction)¶

Univariate Prophet¶

Multivariate Prophet¶

N225 & Oil¶

Weekly Analysis Prophet (6 Monthes Prediction)¶

Univariate Prophet¶

Multivariate Prophet¶

All External regressors¶

only n225¶

oil & usdjpy¶

GDP & Unemp¶

Tunnned Daily Prophet 1 Year Prediction¶

Hyperparameter Tunnning¶

Residuals Check for Prohpet¶

Prediction and Accuracy¶

LSTM Model¶

RNN¶

LSTM¶

Recursive model (ENEOS)¶

Rolling model only applied to the stock ENEOS because the runtime was too long when rolling model run on other stocks we picked¶

Pre-processing¶

Pre-processing & stationarity check¶

Pre-processing for external regressors¶

Data Splitting¶

Function¶

Rolling Univariate ARIMA (3)¶

Rolling Univariate ARIMA (4)¶

Rolling ARIMAX with External Regressors (3) link text)¶

All External regressors¶

only n225¶

oil & usdjpy¶

GDP & Unemp¶

Rolling ARIMAX with External Regressors (4)¶

All External regressors¶

only n225¶

oil & usdjpy¶

GDP & Unemp¶

Rolling VAR¶

All external regressors¶